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http://www.archive.org/details/manualofelementaOOatwa 


MANUAL 


OF 


Elementaky  Logic. 


DESIGNED  ESPECIALLY  FOR  THE  USE  OF  TEACHERS 
AND  LEARNERS. 


BY     / 

LYMAN  H.  ATWATER, 

PROFESSOR    OP   MENTAL   AND    MORAL    PHILOSOPHY    IN    THE 
COLLEGE    OP   NEW   JERSEY. 


-*»*- 


PHILADELPHIA 
J.     B.     LIPPINCOTT    &     CO 

1807. 


Entered  according  to  the  Act  of  Congress,  in  the  year  1867,  by 

J.  B.   LIPPINCOTT  &  CO., 

In  the  Clerk's  Office  of  the  District  Court  for  the  Eastern  District  of 

Pennsylvania. 


CONTENTS. 


PAGE 

Preface 9 


CHAPTER  I. 

THE    SPHERE    AND    OBJECTS    OF    LOGIC. 

Section  I.  Logic  the  Science  of  the  Laws  of  Thought 13 

II.  The  General  Nature  of  Logical  Judgments 22 

III.  Reasoning  as  including  Conceptions  and  Judg- 

ments       25 

IV.  Pure  and  Applied  Logic 2S 

V.  Applied  Logic  further  explained 34 

VI.  Utility  of  Logical  Study 36 

VII.  Fundamental  Axioms  of  Logic 40 

CHAPTER  II. 

CONCEPTIONS. 

Section  I.  Conceptions,  their  Nature  and  Formation 43 

II.  Higher  and  Lower  Conceptions 47 

III.  Genus,  Species,  Essence,  Differentia,  etc 49 

1*  5 


6  CONTENTS. 

PAGE 

Sect.  IV.  Other  Distinctions  in  Genus  and  Species 51 

V.  The  Three  Powers  of  Conceptions 53 

VI.  Inverse  Ratio  of  Extension  and  Intension 55 

VII.  Denomination  of  Conceptions 56 

VIII.  Various  kinds  of  Terms 58 

IX.  Quality  of  Conceptions 64 

X.  Notative  and  Symbolical  Conceptions 67 

XI.  Logical  Division 69 

XII.  Definition 73 


CHAPTER  III. 

JUDGMENT. 

Section  I.  The  Constituent  Parts  of  a  Judgment 82 

II.  Quantity,    Quality,    Relation,    and    Modality   of 

Judgments 87 

III.  Quantity  of  Judgments 87 

IV.  Quality  of  Judgments 89 

V.  Distribution  of  Terms  in  Judgments 91 

VI.  Relation  of  Judgments..... 91 

VII.  Substitutive  Judgments 95 

VIII.  Analytic  and  Synthetic  Judgments 100 

IX.  Modality  of  Judgments 101 

X.  Plurative  Judgments 102 

XL  Conversion  of  Hypothetical  into  Categoricals 102 


CONTENTS.  7 

CHAPTER  IV. 

REASONING IMMEDIATE    INFERENCE. 

TAGE 

Section  I.  Mediate  and  Immediate  Inference  Defined 100 

II.  Immediate  Inference  by  Opposition 107 

III.  Immediate  Inference  by  Conversion 113 

IV.  Otber  Modes  of  Immediate  Inference 117 

CHAPTER  V. 

REASONING — MEDIATE    INFERENCE. 

Section  I.  Introductory  Observations 123 

II.  Moods  of  the  Syllogism * 132 

III.  Its  Four  Figures 133 

IV.  Aristotle's  Dictum  and  other  Maxims 138 

V.  Unfigured  Syllogisms 1-12 

VI.  Hypothetical  Syllogisms 144 

VII.  Conditional  Syllogisms 145 

VIII.  Disjunctive  Syllogisms 146 

IX.  The  Dilemma 148 

X.  Incomplete  Syllogisms 152 

XI.  Complex  Syllogisms 153 

CHAPTER  VI. 

APPLIED   LOGIC — FALLACIES. 

Section  I.  Fallacies,  Formal  and  Material 158 

II.  Fallacies,  partly  Formal  and  partly  Material 166 

III.  Logical  Puzzles 179 


S  CONTENTS. 

CHAPTER  VII. 

APPLIED    LOGIC — METHOD. 

PAGE 

Section  I.  Original  and  Derivative  Sources  of  Knowledge....  186 
II.  Problematic,  Assertory,  and  Apodictic  Judgments,  193 

III.  Deductive  Reasoning 196 

IV.  Inductive  Reasoning 197 

V.  Hypothesis 207 

VI.  Analogy 211 

VII.  Categories 213 

VIII.  Harmony  and  Co-ordination  of  the  Sciences 217 


APPENDIX. 

APPENDIX  A. 
examples  for  logical  praxis.  223 

APPENDIX  B. 

SYSTEMS    OF    SYLLOGISTIC    NOTATION. 

Notation  by  Circles 232 

Notation  by  Straight  Lines 234 

The  Hamiltonian  Notation 236 


PREFACE. 


The  object  of  this  volume  is  to  furnish  a  text-book  of  in- 
struction for  the  use  of  teachers  and  students  of  Elementary 
Logic.  This  object  has  determined  its  contents  and  form. 
It  does  not  claim  to  offer  any  new  contribution  to  the 
science  of  Logic,  as  such,  although  it  is  quite  possible  that, 
in  some  instances,  the  author's  way  of  illustrating  known 
truths  may  have  shed  some  new  light  upon  them.  Still 
less  is  it  designed  to  present  an  exhaustive  treatise  contain- 
ing all  the  truths  pertaining  to  Logic  which  have  been 
reached  by  the  great  masters  and  expounders  of  the  science. 

But,  as  before  stated,  the  object  is  to  present  the  great 
elements  of  the  science  in  a  form  suited  to  the  wants  of 
teacher  and  learner.  Books  for  this  purpose  of  decided 
merit  are  indeed  now  in  use.  Many  of  them,  however,  are 
not  constructed  in  conformity  to  the  now  recognized  con- 
ception of  Logic,  as  the  Science  of  the  Laws  of  Thought. 
Others  are  too  extended,  cumbrous,  or  abstruse,  for  ele- 
mentary instruction,  especially  within  any  time  that  can 
possibly  be  allotted  to  this  study  in  our  Colleges  and  High- 
schools.  Some  of  them  need  much  previous  drill  in  more 
elementary  treatises  as  a  propaedeutic. 


10  PREFACE. 

At  all  events,  the  author  in  this  brief  manual  has  at- 
tempted to  meet  a  want  which  has  become  urgent  in  his 
own  personal  experience  as  a  teacher.  How  far  it  meets 
the  wants  of  others  remains  to  be  seen.  He  can  only  be- 
speak for  it  a  candid  judgment  and  fair  trial. 

It  is  only  just  to  add  that  he  has  freely  used  whatever 
best  served  his  purpose  in  the  works  of  other  authors,  some- 
times without  explicit  mention  of  the  sources  from  which 
he  has  drawn.  It  is  proper,  however,  to  say  that  he  is  in 
greater  or  less  degrees  indebted  to  the  works  of  Whateley, 
Kant,  Hamilton,  Mansel,  Bayne,  De  Morgan,  Wilson, 
Bowen — and  most  of  all  to  Thomson's  Laws  of  Thought. 
He  trusts  this  general  acknowledgment  will  suffice  for  all 
cases  in  which  none  more  specific  is  made. 

Perhaps  no  better  place  will  occur  for  stating,  that  occa- 
sional paragraphs  will  occur  of  such  a  description  that, 
though  important,  they  may  be  postponed  for  review,  or 
omitted  entirely,  if  pressure  for  time  requires.  It  is  of 
course  always  the  teacher's  province  to  judge  how  far  any 
portions  of  the  several  chapters  may  be  wisely  postponed 
until  the  time  of  review.  The  author  will,  however,  sug- 
gest that  Sections  IY.  and  V.,  of  Chapter  I.,  may  advan- 
tageously be  deferred  until  the  student  reaches  Chapter  VI. , 
when  it  will  form  a  suitable  introduction  to  the  study  of 
applied  Logic.  The  beginner  can  better  understand  and 
appreciate  it  at  this  point,  than  in  that  natural  order  in 
which  it  is  treated  in  defining  the  sphere  and  objects  of 
logical  science.  The  same  view  applies  in  a  less  degree  to 
Section  VII.  of  the  same  chapter,  on  the  Uses  of  Logic. 


PREFACE.  11 

Portions  of  this  will  of  course  be  better  understood  after 
the  student  has  learned  somewhat  of  the  principles  involved. 
On  the  other  hand,  it  is  a  strong  reason  for  giving  early 
attention  to  it,  that  some  idea  of  the  advantages  of  the 
study  is  a  strong  stimulus  to  the  student  to  make  the  effort 
necessary  for  its  successful  prosecution. 


ELEMENTARY    LOGIC. 


CHAPTER    I. 

THE   SPHERE   AND   OBJECTS   OF   LOGIC. 

SECTION    I. 

1.  Logic  is  the  science  of  the  laws  of  _    ,  _  _ 

Logic  defined. 

THOUGHT  OR  THINKING. 

2.  Of  these  two  words,  thought  and  thinking, 
we  shall  hereafter  use  the  former  to  denote  the 
object  matter  of  Logic.     Thought  may  Thinking  or 
denote  either  the  process  or  the  product     ^  'JJjj  ob_ 
of  thinking,  i.  e.,  it  may  be  taken  either  jective. 

in  a  subjective  or  objective  sense.  Logic  is  the 
science  of  the  laws  of  thought  in  both  senses;  the 
laws  which  govern  genuine  thinking  itself,  and 
also  the  relations  of  the  products  of  thought  to 
each  other,  and  to  all  matters  to  which  they  are 
applicable. 

3.  Object   means   that    about   which    the   mind 
thinks;  Subject,  the  mind  itself.     The  SnbjectandOb- 

j.      ,•  7  •     ,  •  l     7  •     #•  1  1 1        ject  defined, 

adjectives  subjective  and  objective,  and  the 

2  13 


14  LOGIC.  [Chap.  T. 

adverbs  subjectively  and  objectively,  have  a  corre- 
sponding import ;  the  former  in  each  case  referring  to 
the  mind  considered  as  the  subject  of  conscious  states 
of  knowing,  thinking,  feeling,  willing;  the  latter 
referring  to  whatever  becomes  an  object  of  the 
mind's  attention.  And  since  the  mind  may  make 
itself,  its  own  states  and  exercises,  objects  of  its 
attention,  it  is  said,  in  this  case  to  objectize  itself,  or 
become   a  subject-object.      When   it   is 

Subject-object.  ,„  ,  ,.       .      .  ,,  ,  . 

neediul   to   discriminate   other   objects 

from  this  subject-object,  some  writers  use  the  term 

object-object.    The  student  who  under- 

Object-object.  ,     ',       „  .  .,,         .,  , 

stands  the  foregoing,  will  easily  under- 
stand the  terms  objectively  and  subjectively,  when  they 
come  in  his  way.  The  sooner  these  terms  are  under- 
stood, the  better,  as  they  are  of  constant  occurrence, 
not  only  in  philosophy,  but  in  general  literature. 

4.  The  next  step  in  clearing  the  subject  is  to 
Tbougbt  de-      determine  what  thought  is. 

wwking  and  Thought  is  subjectively  the  operation, 

product  of  tbe  an([  objectively  the  product  of  the  Dis- 

Discursive  Fac- 
ulties, cursive  Faculties  of  the  mind. 

5.  It  becomes  necessary  now,  in  order  to  make 
this  definition  complete  and  intelligible,  to  explain 
what  we  mean  by  the  Discursive  Faculties.  Although 


Sec.  I.]  ITS  SPHERE  AND  OBJECTS.  15 

this  is  properly  within  the  province  of  Psychology, 
yet  it  is  at  one  of  those  points  of  con-  Tlie  Discursive 

Faculties  ex- 

tact  between  it  and  Logic,  which  re-  piained. 
quires  to  be  explained  in  defining  the  object-matter 
of  either. 

6.  For  our  present  purpose  then,  the  faculties  of 
intelligence,  (leaving;;  out  of  view  me-  Twofold  divi- 

s  7    v  r  &  sion  of  Intellec- 

mory   which    retains    and    reproduces  tual  Powers. 
what  is  given  by  the  other  faculties),  may  be  di- 
vided into  two  great  classes — the  Intuitive  and  the 
Discursive. 

7.  The  Intuitive  Faculties  are  those  which  dis- 
cern objects,  phenomena,  or  presentations  immedi- 
ately, and  not  indirectly,  i.  e.,  not  Inttlitive  Fac- 
through  the  medium  of  any  process  of  cities  described. 
thinking.  Thus,  the  objects  perceived  by  the 
senses  are  known  intuitively,  as  whatever  we  see, 
hear,  touch,  taste,  or  smell.  So  also  our  states  of 
consciousness,  our  feelings,  volitions,  cognitions,  at 
the  moment  of  their  occurrence,  are  known  intui- 
tively. The  mind  knows  them  immediately,  intue- 
tur,  by  a  direct  beholding,  and  without  the  inter- 
vention of  reasoning  or  thinking. 

8.  The  Intuitive  Faculties  furnish  us  ^  *"*  , 

the  material  oi 

the  original  material  of  all  our  know-  Thought. 


16  LOGIC.  [Chap.  I. 

ledge.  The  Discursive  Faculties  take  the  matter 
The  Discursive  thus   furnished,  and   proceed  from  it, 

elaborate  it  in- 
to new  forms,      discitrrunt,  to  new  results  founded  upon 

it.     They  work  it  up  or  elaborate  it  into  new  forms; 

Why  called  Ela-  nence  by  Hamilton  and  others,  they  are 
horative.  called  the  Elaborative  Faculties. 

9.  It  is   important   to   observe,   that   intuitions 
intuitions  are    (aside  of  exceptions  in  the  region   of 

of  individual  ob- 
jects, self-evident  supersensual  truths),  that  is 

to  say,  intuitions  of  material  things  or  of  states  of 
consciousness,  are  always  of  individual  objects, 
never  of  classes  of  objects.  By  the  senses  we  per- 
ceive individual  trees,  stones,  or  animals.  But  the 
Further  Intel-     senses  do  not  apprehend  them  in  classes. 

lectualpro-  Tq   clagsif     ig   to   perform  a  pr0CeSS   of 

cesses  are  dis-  J  r  L 

cursive.  Abstraction  and  Generalization,  i.  e.  of 

Thought,  and  goes  beyond  intuition.  So  of  states 
or  acts  of  consciousness.  They  are  first  perceived 
singly,  not  in  classes.  Now  this  pure  intuition  is 
Logic  concerns  not  thought  strictly  so-called,  nor  in 
the  former.  the  sense  here  intended.  It  furnishes 
matter  for  thought,  but  is  not  thought.  With 
this  logic  does  not  concern  itself,  unless  casually 
and  indirectly.     It  develops  the  laws  of  the  think- 


Sec.  I.  ]  ITS  SPHERE  AND  OBJECTS.  yj 

ing  process,  and  of  its  products,  in  their  constituent 
parts,  combinations,  and  relations. 

10.  The   Discursive  Faculties   are  those  which 
take  the  materials  furnished  by  intui-    Discursive 
tion,  and,  by  a  process  of  thought,  in-    Facillties  P™" 

°      '  ceed  by  Ana- 

volving  Analysis  and  Synthesis,  reach    ly»s  and  Syn- 

,  thesis  to  new- 

new  results.      JBirst,   they  separate  or    results. 

analyze  the  single  objects  or  wholes  given  in  intui- 
tion into  parts.  They  notice  one  or  more  of  the 
parts  into  which  any  individual  whole  is  thus 
analyzed,  to  the  exclusion  of  the  residue.  That  is, 
they  abstract  them  from  the  rest.  Thus,  suppose 
that  this  book  be  the  object  beheld.  It  has  exten- 
sion, figure,  solidity,  color,  is  composed  Abstraction  de_ 
of  printed  sheets,  enclosed  in  binding,  scribed. 
and  is  a  treatise  on  Logic,  etc.  Now  the  mind  may 
attend  to  one  or  some  of  these  properties,  neglecting 
the  rest.     This  is  Abstraction. 

11.  Again,  the  mind,  observing  a  number  of  ob- 
jects that  agree  in  one  or  more  particulars  singled 

OUt    by    abstraction,    forms    a    class    Or   Generalization 
n.    -.  .      .         ,  .   ,  „,  illustrated   and 

genus  of  objects  which  so  agree.     Thus,  explained. 
noting  extension,  not  only  in  this  book,  but  in  every 
material  object,  it  classifies  them  as  extended  ob- 
;  sets.     Observing  that,  besides  extension,  they  have 

2  *  B 


18  LOGIC.  [Chap.  I. 

solidity,  it  forms  them  into  the  genus,  bodies  or 
matter.  Noting  also  that  many  of  these  agree  in 
being  composed  of  sheets  of  paper  for  the  purpose 
of  containing  written  or  printed  language,  it  classi- 
fies them  as  such,  under  the  name  of  books.  This 
is  the  manner  in  which  it  forms  genera  or  classes 
from  individual  objects.  And  to  do  this  is  to  gene- 
ralize. It  is  obvious,  moreover,  that  generalization 
may  proceed,  not  only  from  individuals  to  classes, 
but  from  lower  genera  to  higher,  which  comprehend 
them :  as  from  white-oak,  yellow-oak,  scrub-oak, 
live-oak,  to  oak;  and  from  oak,  hickory,  ash,  etc., 
to  tree ;  and  from  tree,  grass,  flower,  grain,  etc.,  to 
vegetable ;  and  so  on,  till  we  arrive  at  the  highest 
possible  generalization  (summum  genus),  which  is 
Being.     Hence  Logic  treats  first, 

OF   CONCEPTIONS.* 

12.  The  product  of  this  Generalization  is  con- 
ception [con  capio)  the  taking  of  many  together  in 

*  This  is  the  meaning  to  which  logicians  now  limit  the  word 
conception,  viz.,  that  act  or  product  of  the  mind  which  is  denoted 
by  a  general  term,  and  is  obtained  by  generalization.  In  common 
speech,  it  has  a  much  hroader  import,  and  is  used  almost  synony- 
mously with  that  loosest  of  words,  idea,  i.  e.  for  almost  any  men- 
tal act  or  representation.     And  by  philosophers  it  has  been  used 


Sec.  I.]  ITS  SPHERE  AND  OBJECTS.  19 

one,  i.  e.  in  one  class,  denoted  by  one  name.  This 
conception  or  the  name  denoting  it,  re-  n 

r  o      7  Conception   ex- 

presents,  not  all  of  any  individual  ob-  Plained- 
ject,  but  so  much  thereof  as  is  common  to  it  with  the 
whole  class  of  which  it  is  one.  Thus  the  concep- 
tion bright  denotes,  not  all  of  any  one  bright  object, 
but  so  much  of  it,  as  it  has  in  common  with  all 
bright  objects. 

13.  This  conception,  or  mental  representation  of 
what  is  common  to  a  plurality  of  ob-  Concrete  and 

.  .  _  Abstract  Gon- 

jects,   may  be   abstract,   or  viewed   by  ceptions, 
itself  irrespective  of  any  objects  to  which  it  belongs, 
as  brightness;  or  concrete,  i.  e.  belonging  to  some 
object,  as  bright  moon. 

14.  It  may  also  be  considered  subjectively  and 
objectively,  either  with  reference  to  the  mental  pro- 

almost  as  vaguely.  Particularly  they  have  used  it  to  denote  the 
mental  similitudes  of  past  cognitions  or  objects  of  cognition  which 
are  raised  in  the  mind  by  the  exercise  of  memory.  As,  when  I 
remember  a  house,  I  have  a  mental  image,  or  as  these  philoso- 
phers would  say,  a  conception  of  it.  So  of  the  products  of  Con- 
structive Imagination — new  combinations,  which  are  not  mere 
copies  or  images  of  any  thing  else.  These,  too,  by  many  authors, 
of  whom  Reid  is  an  eminent  example,  are  styled  conceptions. 
The  strict  scientific  use  of  the  term,  however,  in  present  philo- 
sophic nomenclature,  is  to  signify  the  mental  exercise  or  product 
of  generalization. 


20  LOGIC.  [Chap.  I. 

cess  forming  it,  or  with  reference  to  the  product  of 

Subjective  and  that  process,  considered  as  formed,  and 

jective     on-  ma(je  £jie  0bject  0f  our  thin  kino-.    Some 

ception.      Con-  J  ° 

cept.  writers   limit   the  word   "  conception" 

(conceptio)  to  the  former ;  and  denote  the  latter  by 
the  word  "  concept"  (conceptus).  And  as  logic,  in 
evolving  the  laws  of  this  product  of  thought,  makes 
it  the  object  of  attention,  these  writers  use  the  word 
"  concept"  exclusively  to  denote  this,  which  is  the 
primary  element  within  this  sphere  of  this  science. 
Since,  however,  this  word  serves  no  purpose  not 
equally  well  accomplished  by  the  word  "concep- 
tion," we  shall  adopt  the  latter  to  denote  the  first 
object-matter  that  falls  within  the  sphere  of  the 
science  of  logic,  i.  e.  the  products  of  Abstrac- 
Generaiization    tion  and  Generalization ;  of  which,  be  it 

involves  Ab- 

straction.  observed,  in  passing,  the  former  may 

take  place  without  the  latter,  but  not  the  latter 
without  the  former. 

15.   Conceptions,   and,   indeed,   the   whole  pro- 
Conceptions  in-  cess  0f  generalization,  are  incomplete, 

complete  with- 

out  names.  fugitive,  and  unavailable,  until  they 
are  set,  and  so  to  speak,  encased  and  preserved  in 
names.  Each  one  may  easily  test  this  for  himself, 
by  an  examination  of  his  own  consciousness.     He 


Sec.  I.]  ITS  SPHERE  AND  OBJECTS.  21 

will  see  that  he  cannot  retain,  or  employ,  to  any 
extent,  in  judgments  and  reasonings,  the  ideas  or 
conceptions  denoted  by  general  words,  without  the 
words  themselves.  The  attempt  to  preserve  and 
turn  to  account  our  generalizations  without  naming 
them,  has  well  been  likened  to  the  process  of  making 
conquests,  and  leaving  them  without  fortifications 
for  their  security  and  preservation. 

16.  Hence,  as  terms  are  so  implicated  with  the 
conceptions  for  which  they  stand,  we  Terms  and  Con- 

„  ,  .  ceptions    inter- 

may  often  use  the  two  interchangeably,  changeable. 

The  older  logicians  were  wont  more  commonly  to 
use  the  former  when  treating  of  this  department  of 
their  science.  Some,  of  whom  Whateley  is  a  promi- 
nent example,  have  carried  this  view  to 
the  extreme  of  maintaining  that  Logic 
is  wholly  conversant  about  language.  This  has 
been  pronounced  by  others,  as  Hamilton,  to  be 
utterly  groundless.  The  truth  is,  assuredly,  that 
logic  is  primarily  and  properly  conversant  about 
thought,  and  about  language  incidentally  as  the 
vehicle  of  thought.  The  science  of  language  is 
Grammar,  or  Philology,  and  not  Logic,  which  is 
the  science  of  the  laws  of  thought. 

17.  And  yet,  owing  to  the  inseparable  connec- 


22  LOGIC.  [Chap.  I. 


tion,  amounting,  for  practical  purposes,  to  almost 

Sense  in  which  ail  identification  of  thought  and  lan- 
Whateley's  doc- 
trine is  true.       guage>   there   is  a   sense   obviously,    in 

which  Whateley's  doctrine  may  be  regarded  as  a 
half  truth — often  the  worst  form  of  error.* 

18.  The  first  part  of  Logic  then  has  to  do  with 
The  first  part  of  that  product  of  thought  which  results 

Los;ic  deals  with    n  i«      ,•  n   j  /"i  li 

n  b  irom  generalization,  called  Conception ; 

Conceptions  or  ©  r  > 

Terms.  and  with  terms  or  names  incidentally, 

as  being  the  vehicles  of  conceptions. 

The  next  of  the  Discursive  Faculties  is  Judgment. 
And  it  gives  as  its  products  the  second 
great  object  of  logical  science,  to  which 

we  now  proceed. 

Sect.  II.    Logical  Judgments. 

19.  We  say  Logical  Judgments,  because  there  is 

Logical  and  a  sense  in  which  judgment  is  a  con- 
Primitive  Judg-  ,. 
ment  compared,  stituent  ot  every  act  oi  mind  or  exer- 
cise of  consciousness.  If  we  have  a  pain  we  can- 
not but  judge  that  we  have  it.  Consciousness  is 
the  knowledge  of  our  mental  operations,  and  in- 
separable from  them.      Of  course,  the  knowledge 

*  This  interpenetration  of  thought  and  language  may  go  far  to 
reconcile  and  clear  up  the  dispute  between  the  Nominalists  and 
Conceptualists. 


Sec.  IL]  ITS  SPHERE  AND  OBJECTS.  23 

that  we  have  them,  is  in  some  sense,  a  judgment 
that  we  have  them.  For  distinction's  sake  this, 
which  enters  into  all  the  intuitions  of  the  mind, 
may  be  called  Primitive  Judgment.  It  Primitive  Judg- 
furnishes  the  materials  out  of  which  ^^^ 
conceptions  and  logical  judgments  are  ence. 
ultimately  framed.  The  only  predicate  which  it 
gives  is  that  of  existence.  It  simply  affirms  that  a 
given  phenomenon  external  or  internal  is. 

20.  Logical  Judgment,  on  the  other  hand,  in- 
cludes a  conception  as  one,  or  concep-  Logical   jn(ig_ 
tions  as  both,  of  its  elements.     It  com-  ^ent  defined. 
pares  two  conceptions,  or  a  conception  and  an  in- 
tuition, and  affirms  that  they  agree  or  Compares  Con- 
disagree.     Thus  it  affirms  of  the  con-  ^^2d£ 
ception  "man"  and  the  conception  "ra-  tuitions. 
tional,"  that  they  agree,  i.  e.  that  "  man  is  rational." 
So  likewise  of  horse  and  quadruped,  tree  and  plant, 
etc.,  etc.     Or  if  we  take  an  individual  object  of  in- 
tuition named  Pompey,  and  the  conception  man,  or 
horse,  as   the   case   may  be,  we   may  affirm   that 
"  Pompey  is  a  man  f  "  Pompey  is  a  horse."     And 
negatively,  we  may  affirm  that  the  conceptions  man 
and  quadruped  do  not  agree ;  "  man  is  not  a  quad- 
ruped;" that  the  particular  object  called  Pompey 


24  LOGIC.  [Chap.  I. 

and  the  conception,  philosopher,  do  not  agree. 
Pompey  is  not  a  philosopher.  Similar  examples  of 
all  these  forms  of  judgments  the  reader  can  easily 
multiply  at  his  pleasure. 

21.  Remarking  here  provisionally,  that  a  judg- 
Terms,  Subject  ment   consists  of  two  parts   or  terms 

and  Predicate 

defined,  (termini,  extremes)  the  Subject,  or  that 

which  is  spoken  of,  and  the  Predicate  or  that  which 
is  said  of  the  subject,  it  follows  from  this  defini- 
The  Predicate     tion,   that  while   the   subject   may  be 

always  a  con- 
ception, either  an  intuition  or  conception,  the 

predicate  must  always  be  a  conception  or  common 

term,  the  name  of  a  class.    If  we  have  Peter  for  the 

subject,  unless  we  have  a  common  term  as  predicate, 

we  can  get  only  the  senseless  tautological  judgment, 

Peter  is  Peter.     Of  judgments  it  is  unnecessary  now 

to  say  more,  in  marking  out  the  sphere  of  Logic, 

than  that  they  constitute  the  second  great  product 

of  thought,  and  object  of  Logic  as  the  science  of  the 

laws  of  thought. 

22.  From  Judgments  the  mind  proceeds  to  de- 
The  mind  pro-  rive    other   judgments    founded    upon 

ceedsfromjndg-  rpi  •     •      -o  •  •    £ 

ments  to  new  them,  ihis  is  .Reasoning,  or  inference 
judgments         from  premises  to  conclusion.     Thus  to 

founded  upon 

them.  conclude   from  premises  is  in  fact  to 


Sec.  III.]  ITS  SPHERE  AND  OBJECTS.  25 

judge.     So  all  modes  of  thought,  from  conceptions 
to  reasonings  are  in  reality  forms  of  -6-11  thought  ia 

.     t  rru  .    n  reality  a  form 

judgment.     The   third  and  last  great  0f  judgment. 
province  of  Logic,  therefore,  is  the  laws  of  rea- 
soning. 

Sect.  III.    Reasoning. 

23.  This  runs  into  various   branches  or  modes, 
Mediate    and    Immediate,  Categorical  The  third  pro- 
and  Hypothetical,   which  need  not  be  Seasoning. 
further  denned  nor  explained  till  we  come  to  treat 
of  it  in  form  and  in  length. 

Until  a  recent  period,  it  was  largely  the  custom 
of  logicians  to  treat  Reasoning  as  constituting  the 
whole  primary  object-matter  of  their  Former  place  of 
science,  and  to  bring  Judgments  and  f^H* 

'  &  &  Logical  Trea- 

Conceptions,  under  the  name  of  Propo-  tises. 
sitions  and  Terms,  into  the  sphere  of  Logic,  only 
on  the  ground  of  their  being  elements  of  the  Syl- 
logism and  other  forms  of  reasoning.  But  they  in- 
variably treated  of  these  terras  and  judgments  in 
many  aspects  of  the  first  importance,  which  are  not 
immediately  essential  to  the  Syllogism,  or  other 
forms  of  Reasoning.  Thus  Whateley  has  a  short 
introductory  chapter  in  explanation  of  terms  (con- 
ceptions), so  far  as  their  relation  to  forms  of  reason- 


26  LOGIC.  [Chap.  I. 

ing  is  concerned,  while  he  postpones  the  considera- 

Conceptions  and   tion  °f  them  in  chief>  tiU  he  has  finished 

Judgments        tne  analysis  of  the  various  forms  of  the 

have  a  place  in 

Logic  in  their  Syllogism.  This  shows  that  these  con- 
ceptions and  judgments  have  a  separate 
and  independent  place  in  Logic  on  their  own  account, 
and  in  their  own  right,  irrespective  of  their  place 
in  the  Syllogism.  This  will  be  more  evident  when 
the  student  reaches  these  subjects.  Indeed,  it  is  only 
necessary  to  think  of  Genus,  Species,  Differentia, 
Essence,  Accident,  Absolute,  Relative,  Correlative, 
etc.,  as  applicable  to  Conceptions,  to  see  that  these 
have  in  their  own  right,  a  leading  place  in  the 
science  of  Logic.  The  definition  of  Logic,  till  re- 
cently in  vogue,  as  being  the  science  of 

Recapitulation. 

Reasoning,  is  therefore  too  narrow.     It 

is,  as  we  have  defined  it,  and  as  the  present  masters 

of  the  science  generally  define  it, 

Definition  of  I-    THE   SCIENCE   OF   THE   LAWS  OF 

Logic.  Thought. 

II.  Thought  is  the  operation,  or  product 

OF  THE   OPERATION,   OF   THE   DlSCUR- 

Of  Thought. 

sive  Faculties,   as  distinguished 
from  the  Intuitive. 


See.  III.]  ITS  SPHERE  AND  OBJECTS.  27 

III.  The  Discursive  Faculties  are, 

a.  Abstraction  and  Generalization ;  the  product 
of  Avhich  is  Conception. 

Enumeration  of 

b.  Judgment,  which   out  of  Concep-   Discursive  Fac- 

Til  TIP^I 

tions  forms  Logical  Judgments. 

c.  Reasoning  which  from  judgments  given  evolves 

other  judgments  founded  upon  them. 

The  thinking  and  products  of  think-  LoSic  deals 

with  Concep - 

ing,  whose  laws  Logic  unfolds,  therefore,  tions,  Logical 

^  x  T  Judgments,  and 

are,    Conceptions,    Logical    Judg-  Rea°onings'. 
ments,  Reasonings.* 

*  I  also  rank  Constructive  Imagination  among  the  Discursive 
Faculties.  Its  operations  and  products,  therefore,  are  of  the  na- 
ture of  thought.  As  we  unfold  the  laws  of  thought,  it  will  ap- 
pear that  they  cannot  be  violated,  even  in  the  creative  works  of 
this  faculty.  They  may  be  violated  in  the  apparent  form,  sound, 
and  sense  of  the  language  employed,  and  the  imagery  constructed; 
but  not  in  its  real  interior  significance.  All  appearance  of  thought 
which  violates  these  laws,  is  not  genuine  thought,  but  a  counter- 
feit or  simulation  of  it.  The  creations  of  imagination  cannot 
abolish  the  laws  of  Conception,  Judgment,  Reasoning.  They  can- 
not legitimate  contradictions,  render  a  round-square  possible  or 
conceivable,  or  make  arguing  in  a  circle  valid.  If  it  tells  us  that 
rain-drops  are  the  tears  of  the  sky,  it  means  such  resemblance 
between  the  tears  and  rain-drops  as  actually  exists.  The  laws 
of  Logic,  therefore,  so  far  as  applicable  to  Constructive  Imagina- 
tion, are  developed  in  treating  of  Conceptions,  Judgments,  and 
Reasonings. 


28  LOGIC.  [Chap.  I. 

Sect.  IV. — Pure  and  Applied  Logic* 

24.  Having  defined  the  sphere  of  Logic,  and 
pointed  out  the  matters  with  which  it  deals,  it  re- 
mains that  we  further  elucidate  it,  by  showing  what 
it  is  in  itself  considered  as  pure  science,  in  distinc- 
tion from  the  application  of  its  principles  to  the 
investigation  of  truth  and  the  ascertainment  of  facts 
— Pure  and  Applied  Logic. 

Pure  Logic  treats  of  the  Laws  of  Thought 
Pure  Logic        as  they  are  in  themselves,  whatever  be 

deals  with  the  . 

laws  of  Thought  the  object-matter  to  which  they  are  ap- 
lrrespective  of    pjje(j  an(j  irrespective  of  their  applica- 

their  Applica-     l  '  l  ri 

tions.  tion  to  any  case  of  actual  being.     Its 

principles  and  laws,  like  those  of  Pure  Mathema- 
tics, are  true  in  themselves,  irrespective  of  their 
application  to  cases  of  actual  being,  nay,  whether 
there  be  any  actual  being  to  which  they  are  appli- 
cable or  not.  The  laws  of  the  Syllogism,  the  con- 
ditions of  valid  reasoning,  the  principles  which 
determine  genus,  species,  differentia,  essence,  logical 
division  and  definition,  are  the  same,  whatever  be 

*  This  and  the  following  chapter  may  he  passed  with  advan- 
tage for  the  present,  to  be  taken  up  as  an  introduction  to  Chapter 
VI.  on  Applied  Logic. 


Sec.  IV.]  ITS  SPHERE  AND  OBJECTS.  29 

the   objects   to  which   they  are   applied,  whether 

angels,  men,  animals,  plants,  or  grains  of  sand; 

and  aside  of  such  applications. 

In  this  Logic  classes  with  Mathematics,  and  with 

strict  Metaphysics.     The  rules  of  Arith-  it  classes  with 

metic,  and  the  propositions  of  Geometry  ^uxe    ,a  ,^a" 
7  r     r  J    tics  and  Meta- 

are  true,  irrespective  of  their  applica-  physics. 
tions  to  actual  being,  and  in  respect  to  whatever 
kinds  of  actual  being  furnish  the  conditions  to  which 
they  are  applicable.  The  Multiplication  table  is 
true  in  itself,  irrespective  of  any  actual  being,  and 
in  regard  to  all  actual  being  to  which  it  is  appli- 
cable. 12X12  =  144.  This  of  itself,  however,  does 
not  prove  any  truth  of  actual  being.  It  does  not 
prove  that  there  are  twelve  persons,  each  twelve 
years  old.  But  it  does  prove,  that  if  there  are 
twelve  such  persons,  their  aggregate  age  is  144 
years.     Logic,  as  such,  does  not  concern 

..,/>       .,i,i  ..,  n.  Does  not  in  it- 

ltseli  with  the  original  sources  ot  our  self   •  e  ori  . 
knowledge  of  actual   being,  or  of  the  nal  knowledge 

of  actual  being, 

conditions  to  which  it  applies.  These 
may  be  supplied  by  intuition,  or  testimony,  or  legit- 
imate logical  deduction  from  them.  They  may,  in 
various  aspects,  come  within  the  province  of  Psy- 
chology, Metaphysics,  Ontology,  or  the  different 
3* 


30  LOGIC.  [Chap.  I. 

departments  of  physical  science.  But  from  what- 
ever sources  the  requisite  conditions  of  actual  being 
are  furnished,  to  which  any  of  the  principles  of 
Logic  apply,  the  corresponding  consequence  neces- 
sarily follows.  Logic  does  not  prove  that  gold  is 
fusible,  or  that  gold  is  a  metal ;  but  given  these 
truths  from  whatever  source,  and  it  follows  that 
some  metal  is  fusible,  on  principles  of  Logic. 

25.  Hence,  pure  Logic,  like  pure  Mathematics,  is 
a   science    of   necessary   principles    or 

It  is  a  science    ,       ,1  -r»  n     , 

of  necessary  truths.  By  necessary  we  mean  that, 
truths. "  Neces-  the  opposite  of  which,  the  mind  cannot 

sary"  defined. 

conceive  to  be  true  without  intellectual 
suicide.  Such  are  the  following,  "  that  the  whole 
is  greater  than  a  part,"  that  "  all  qualities  must 
belong  to  some  substance,"  that "  no  two  straight 
lines  can  enclose  a  space."  So,  as  in  the  proper 
place  the  student  will  more  fully  see,  that  there  can 
be  no  valid  conclusions  in  a  syllogism  vitiated  by 
negative  premises,  illicit  process,  or  undistributed 
middle ;  that  every  relative  supposes  a  correlative, 
that  we  may  predicate  of  a  species  its  genus  and  dif- 
ferentia; these,  with  all  other  laws  of  pure  Logic,  are 
necessary  truths.  They  are  not  only  true  in  parti- 
cular cases,  but,  when  understood,  it  is  seen  that 


Sec.  IV.]  ITS  SPHERE  AND  OBJECTS.  ^1 

they  must  be  true,  as  the  rules  of  Arithmetic  and  the 

propositions  of  Euclid  must  be  true  in  all 

TT  t       •     •  ,        i  Logic  the   sci- 

cases.   Hence  pure  Logic  is  not  only,  as  ence  of  the  ne_ 
before  shown,  the  science  of  the  laws,  cessary laws  °f 

Thought. 
BUT     OF    THE    NECESSARY     LAWS     OF 

THOUGHT. 

26.  This  characteristic  classes  Pure  Logic  with  the 
a  priori,  as  distinguished  from  the  a  pure  Logic  an  a 
posteriori  sciences.     By  a  priori  know-  Priori  science- 
ledge  is  meant  that  which  is  known  from  conditions 
given,  without  needing  verification  from 

Definition  of  a 

experience.  A  posteriori  knowledge  priori  and  a  pos- 
depends  upon  experience  for  proof.  terior1. 
The  axioms  and  propositions  of  Geometry  are  a 
priori,  because  they  are  known  and  proved  inde- 
pendently of  experience.  The  physical  and  induc- 
tive sciences,  on  the  other  hand,  are  a  posteriori, 
because  they  are  dependent  on  experience  for  proof. 
Hence,  all  sciences  of  necessary  truth,  including 
Logic,  are  a  priori,  for  they  not  only  show  what  ex- 
perience has  proved  true ;  but  what  ever  must  be 
true  in  all  possible  experience,  and  must  condition 
that  experience.  We  know  a  priori,  that  no  two 
straight  lines  can  enclose  a  space,  and  that  every 
equiangular  triangle  must  be  equilateral.     So  we 


32  LOGIC.  [Chap.  I. 

know,  as  the  student  in  the  proper  place  will  see, 
that,  as  the  Extension  of  a  conception  increases,  its 
Intension  must  diminish,  and  vice  versa :  and  that 
there  can  be  no  conclusion  from  negative  premises. 
27.  It  is  putting  the  same  thing  in  another  light, 
to  say  that  the  laws  developed  by  Logic,  are  those 
which  are  necessary  to  the  very  form  of 

Logic  deals  J  J  ^ 

with  the  Forms  thinking,  whatever  be  the  subject-mat- 
mg'  ter  about  which  we  think,  and  indepen- 
dently of  such  subject-matter.  The  forms  of  think- 
ing in  Conceptions,  Judgments,  and  Reasonings, 
are  the  same,  whether  applied  to  planets  or  to 
worms ;  just  as  the  forms  of  Arithmetical  Addition, 
Subtraction,  &c,  are  the  same,  to  whatever  they 
may  be  applied :  and  the  opposite  sides  of  a  paral- 
lelogram are  equal  whether  it  be  on  wood,  slate, 
iron,  or  between  lines  imagined  in  pure  space. 
This  truth  is  set  forth  by  saying  that  Logic  is  the 
science  of  the  forms  of  thought ;  or  of  the  formal 
laws  of  thought — either  phrase  will  serve  our  pur- 
pose sufficiently  well.  And  so  combining  all  the 
elements  thus  far  shown  to  be  comprised  in  the 
essence  of  Logic,  we  reach  this  definition :   Puke 

Completed  defi-    LOGIC  IS  THE  SCIENCE  OF  THE  NECES- 
nition  of  Logic.   SARY  AN  J)  FORMA  I,  LAWS  OF  THOUGHT. 


Sec.  IV.]  ITS  SPHERE  AND  OBJECTS.  33 

Those  sciences,  the  Mathematics,  Logic,  and,  with- 
in certain  limits,   Metaphysics,  which  other  Formal 
deal  with  truths,  not  within  themselves  Sciences- 
originally  implying  actual   being,  but  which   are 
forms  regulative  of  such  actual  being  as  presents 
the   conditions   to   which   they   apply,   are   called 
Formal  Sciences.     Those  on  the  other  hand  which 
have  what,  in  these  relations,  is  called  Fom)  0ontent> 
Content,    or    matter    of   actual   being:,  Matter- 
whether  in  the  realms  of  body  or  spirit,  are  called 
Material  Sciences.      The  contrast  here  Material  gcien. 
is  not  between  Material  and  Spiritual,  ces- 
but  between  Material  and  Formal.     The  opposite 
of  Spiritual  is  Physical  Science.     Mat- 
ter  and  Material  in  these  connections  £££?£ 
refer  to  substances  and  phenomena  of  t0  Physical  Sci- 
actual  being,  whether  bodies  or  spirits. 
Accordingly,   pure   Logic   is   one   of  the   Formal 
Sciences. 

28.  These  are  also  sometimes  named  Hypotheti- 
cal Sciences ;  because  they  prove  truths 

#  Hypothetical 

of  actual  being  only  on  the  hypothesis.  Sciences  ex- 

that  the  conditions  of  actual  being  are  p  ame  ' 
given  to  which  they  are  applicable.     Thus,  that  the 
angle  in  a  semi-circle  is  a  right-angle  proves  no 


c 


34  LOGIC.  [Chap.  I. 

fact  of  actual  being,  until  we  have  some  substances 

in  the  form  of  a  semi-circle,  with  an  angle  inscribed 

in  it.     Such  an  angle  we  know  must  be  a  right 

angle. 

Sect.  V. — Applied  Logic. 

29.  In  the  actual  investigation  of  truth,  we  must 
go  beyond  Pure  Logic,  which,  of  itself,  like  Mathe- 
matics, deals  only  with  forms  of  thought,  and  has 
Pure  Logic  a  n0  content  of  actual  being.  Yet,  like 
calculus.  Mathematics,  it  is  of  the  utmost  value 

as  an  instrument  or  calculus  in  the  investigation  of 
truth.  The  primary  facts,  which  lie  at  the  basis  of 
astronomical  science,  were  not  obtained  by  mathe- 
matics but  by  telescopic  observation.  Mathematics 
is  an  instrument  for  determining  what  is  fairly  in- 
volved in,  or  results  from  these  facts  so  observed. 

.    lication  of  -^  ^s  use  ^ne  f°rmer  science  has  made 

Formal  Scien-    the  immense   strides  which    have   ad- 

ces  to  facts  a  . 

meaus  of  dis-  vanced  it  to  its  present  perfection.     So 

coveriug  truths.  Geometry  and  Trigonometry  will  not  of 
themselves  make  a  science  or  art  of  Navigation, 
Surveying,  or  Engineering.  They  cannot  furnish 
the  facts  which  underlie  these  sciences.  But  the 
application  of  these  Mathematics  to  facts  otherwise 


Sec.  V.]  ITS  SPHERE  AND  OBJECTS.  35 

discovered,  is  indispensable  in  these  sciences,  and 
alone  makes  them  possible. 

30.  So  is  it  with  the  laws  of  Thought  unfolded 
by  Logic.  They  do  not,  of  themselves,  prove  any 
original  fact  of  existence ;  but,  given  such  data,  as 
are  furnished  by  other  means,  it  is  an  instrument 
for  showing  what  is  and  what  is  not  fairly  contained 
in  them  :  for  unfolding  explicitly  what  is  involved 
implicitly :  for  guarding  us  against  unwarranted 
conclusions  from  given  facts  or  truths ; 

n  .  -1 .  ,      .,  .-,  (*(*>,      Uses  of  Logici 

lor  guiding  us  to  the  avoidance  01  fruit- 
less, and  the  adoption  of  fruitful  methods  of  inquiry 
in  the  realms  of  actual  being.     Such  use  of  the  prin- 
ciples of  Logic  in  assisting  us  to  right,  and  pre- 
serving  us   from   wrong   processes   of  thought  in 
our  search  after  truth,  is  what  is  meant  A   lied  Lo  ic 
by  Applied  Logic.     This  has  two  de-  defined. 
partments. 

31.  a.  The   doctrine  of  Fallacies.     Showing 

the   various  ways   in   which   men    consciously    or 

unconsciously   employ,    a    mimicry  of 

.i  i,  .   -,-,        r,  .         p,i       Its  two  depart- 

thought,  especially  of  reasoning,  for  the  ment3i    /alla. 

things  themselves,  thus  sometimes  im-  cies  and  Me" 

thod. 
posing  upon  themselves,  or  essaying  to 

impose  on  others. 


36  LOGIC.  [Chap.  I. 

b.  The  doctrine  of  Method,  or  the  right  way 
to  ascertain  the  truth,  by  modes  of  investigation, 
not  contrary  to,  but  harmonious  with  the  laws  of 
Thought. 

32.  Pure  Logic  then  treats  of  the  formal  and 
necessary  laws  of  Thought  in  Conceptions,  Judg- 
ments, and  Reasonings.     Applied  Logic  deals  with 

the  application  of  these  laws  to  the  de- 
Summation. 

tection  of  Fallacies,  and  the  develop- 
ment of  a  proper  Method  for  the  investigation  of 
Truth.  Before  proceeding,  however,  to  the  formal 
consideration  of  each  of  these  topics,  we  will  make 
a  few  preliminary  observations,  first  on  the  utility 
of  the  study  of  Logic,  and  secondly  on  the  funda- 
mental principles  or  axioms  of  the  science. 

Sect.  VI. — Utility  of  Logical  Study. 

33.  The  study  of  Logic  is  useful  as  means  of 

disciplining  and  invigorating  the  mind. 

Uses  of  Logic. 

intellectual       Few  studies  more  effectually  promote 
wcip  me.         habits  of  attention,  discrimination,  and 
continuous  application. 

34.  The   knowledge  thus   acquired   is   of  high 

Imparts   valu-  vame  on  ^s  own  account.     All  know- 
able  knowledge,  ledge  is  precious  and  elevating ;  but  es- 


Sec.  VI.]  ITS  SPHERE  AND  OBJECTS.  37 

pecially  that  which  sheds  light  on  the  laws  of  our 
thinking,  our  intelligent  and  rational  nature. 

35.  It  is  invaluable  as  furnishing  the  nomencla- 
ture, the  Technical  Terms,  which  define 

Furnishes     apt 

the  products  and  relations  of  true  Technical 
Thought,  and  the  nature  of  the  fallacies  ems' 
which  counterfeit  it.  The  possession  of  these  names 
in  a  multitude  of  cases  will  instantly  suggest  to  the 
mind  the  clew  to  difficulties  which  would  otherwise 
perplex  it.  The  very  terms,  genus,  differentia,  peti- 
tio  principii,  ignoratio  elenchi,  arguing  in  a  circle, 
will  of  themselves  often  suggest  an  analysis  or  ex- 
planation of  perplexities  which  otherwise  might 
long  be  insoluble. 

36.  Generally,  as  a  guide  to  right,  and  a  pre- 
ventive and  corrective  of  spurious  G  ., 
thinking,  i.  e.  of  the  aimless,  erratic,  and  Thinking. 
abortive  exercise  of  our  faculties.  So  it  is  a  pro- 
paedeutic to  all  other  sciences.  It  furnishes  a 
needful  training  for  every  department  of  study.  So 
it  has  been  crowned  by  some,  as  scientia  scientiarum, 
by  others,  as  ars  artium. 

37.  The  question  has  been  much  discussed  whether 
Logic  is  a  Science  or  an  Art.     But  as  Logic  a  Science, 

the  end  of  Science  is  to  know,  and  of  Art, 
4 


38  LOGIC.  [Chap.  I. 

Art  to  do,  or  rather  to  make  a  product  which  sur- 
vives the  making,  so  there  can  be  no  doubt  that 
pure  Logic  is,  like  pure  Mathematics,  properly  a 
Science;  while  Applied  Logic,  like  Applied  Mathe- 
matics, may  afford  great  light  in  the  learning  and 
executing  of  the  arts  to  which  it  is  applicable,  as 
the  art  of  Reasoning,  Rhetoric,  and  Oratory.  Al- 
though not  useful  as  in  itself  an  art,  it  is  useful  as 
furnishing  light  and  guidance  in  the  noblest  arts. 
38.  The  study  of  Logic  as  the  science  of  the  Laws 
of  Thought,  gives,  in  fact,  if  not  in  form, 
choiogTof  Dis-  the  knowledge  of  Psychology,  so  far  as 
cursive  Pacul-  ^}ie  faculties  of  Thought  are  concerned. 

ties,  ° 

Although  the  necessary  and  formal  laws 
which  all  true  Thought  must  obey,  are  not  of  them- 
selves psychological  phenomena,  yet  it  is  impossible 
to  master  them,  in  their  application  to  the  pheno- 
mena of  the  Discursive  Faculties,  without  so  far 
forth  understanding  the  psychology  of  those  faculties. 
So  far  as  Abstraction,  Generalization,  Conception, 
Judgment,  Reasoning,  are  concerned,  little  remains 
to  be  learned,  which  is  not  acquired  in  a  thorough 
course  in  Logic,  in  the  present  acknowledged  scope 
of  that  science.  It  is  easy  for  the  teacher,  with  little 
addition  of  labor,  to  compass  this  portion  of  psycho- 


Sec.  VI.]  ITS  SPHERE  AND  OBJECTS.  39 

logy,  in  connection  with  his  regular  course  in  Logic 
— a  matter  of  some  moment,  in  view  of  the  scanty 
time  generally  allowed  to  those  subjects. 

39.  It  has  indeed  been  said  that  men  reason, 
whether  they  know  Logic  or  not.  They  are  not 
dependent  on  Logic  to  confer  on  them  the 

Objections  of 

power  of  reasoning.  Even  Locke  is  Locke  and 
guilty  of  such  poor  burlesque  on  this  others  refuted' 
high  subject,  as  the  following.  "  God  has  not  been 
so  sparing  to  men  to  make  them  barely  two-legged 
creatures,  and  left  to  Aristotle  to  make  them  ra- 
tional. .  .  .  God  has  been  more  bountiful  than  so ; 
He  has  given  them  a  mind  that  can  reason  without 
being  instructed  in  methods  of  syllogizing,"  etc.* 
This  is  quite  as  relevant,  as  if  one  should  say,  "God 
has  not  been  so  sparing  of  gifts  to  men, 

r  fe         fe  '   Analogy  of 

as  to  leave  it  merely  to  the  gramma-  Grammar    and 

x  f      ±i~        jft      n  1  1       Rhetoric^ 

nans  to  confer  the  gilt  01  speech,  or  to 
the  rhetoricians  to  confer  the  gift  of  composition 
and  oratory."  The  science  of  Grammar,  of  course, 
does  not  confer  the  gift  of  speech.  It  presupposes 
that  gift.  But  that  it  helps  to  the  correct  use  of 
language,  who  will  dispute  ?   Rhetoric  does  not  first 

*  Quoted  by  Whateley — Logic.     Harper's  Edition,  y>.  37. 


40  LOGIC.  [Chap.  I. 

make  men  eloquent;  but  who  can  doubt  that,  rightly 
used,  it  will  greatly  augment  this  gift  of  elo- 
quence in  those  naturally  endowed  with  it  ?  Logic 
does  not  impart  the  power  of  reasoning  or  thinking. 
But  who  will  question  that  it  greatly  assists  in  de- 
tecting and  avoiding  the  spurious  counterfeits  of 
them ;  and  that  it  is  every  wTay  a  great  intellectual 
tonic?  Locke  is  not  alone,  even  among  men  of 
mark  in  philosophy  and  literature,  in 
this  vulgar  and  Vandal  disparagement 
of  Logic,  which,  if  admissible  against  this,  is  valid 
against  all  liberal  study,  discipline,  and  culture. 
No  less  a  man  than  Macaulay  has  allowed  himself 
to  indulge  in  reflections  and  implications  of  like 
force  and  effect  in  regard  to  Grammar  and  Rhetoric 
as  well  as  Logic.5 


* 


Sect.  VII.  Fundamental  Principles  or  Axioms  op 
Logic,  from  which  all  its  Particular  Laws  Flow, 
or  by  which  they  may  be  tested. 

40.  These   are   commonly  reduced  to  the  four 

following  —  Identity,     Contradic- 
ts Four  Fun-  & 

damental  Frin-   TION,   EXCLUDED    MlDDLE,  AND   SUF- 

*    '  ficient  Reason. 

*  See  Essay  on  Lord  Bacon. 


Sec.  VII.]  ITS  SPHERE  AND  OBJECTS.  41 

I.  The  principle  of  Identity,  which  amounts 
simply  to  this :  that  we  may  affirm  of 

Identity. 

objects  that  they  are  what  they  are. 
This  lies  at  the  foundation  of  all  Positive  Concep- 
tions, and  Affirmative  Judgments,  and  Reasonings. 
Thus  if  the  Conception  rational  be  a  part  of  the 
Conception  man,  we  may  affirm  that  "  man  is  ra- 
tional." On  the  same  ground,  we  may  have  the 
Conception  "rational  animal,"  because  these  may 
concur  in  the  same  being. 

II.  Contradiction.  That  is  we  may  not 
affirm  the  co-existence  of  Conceptions 

..  ,  ,.  Contradiction. 

or  attributes  that  are  mutually  contra- 
dictory, as  "round-square,"  "triangular  parallelo- 
gram," "  good  wickedness." 

III.  Of  two  contradictions  one  must  -n   ,  ,  ,  ,,., 

Excluded  Mid- 

be  true,  and  the  other  false.    There  can  die. 

be  no  medium  between  these.     This  is  the  Law  of 

Excluded  Middle. 

IV.  For  every  conclusion,  affirmation,  or  nega- 
tive, there  must  be  a  Sufficient  Rea-  gufficient  Eea. 
son  or  Ground.     It  must  be  evinced  son- 

by  self-evidence,  or  other  sufficient  evidence. 
4* 


42  LOGIC.  [Chap.  I. 

41.  These  principles  may  seem  too  obvious  and 
Importance  of  familiar  to  be  the  foundation  of  any 
these  principles,  important  science.  But  we  must  bear 
in  mind,  that  the  highest  sciences  are  but  develop- 
ments from  a  few  simple  elements  or  axioms.  The 
science  of  Mathematics  is  but  a  development  or 
evolution  of  a  few  axioms  as  simple  as  the  fore- 
going. Herein,  very  largely,  lies  its  adamantine 
strength.  What  are  the  laws  which  keep  the  myriads 
of  orbs  harmoniously  circling  in  the  depths  of  space, 
but  developments  and  applications  of  the  simple 
but  great  law  of  gravitation?  And  does  not  the 
highest  of  authorities  teach  us  that,  on  the  simple 
obligation  to  love  God  with  all  the  heart,  mind, 
soul,  and  strength,  and  our  neighbor  as  ourselves, 
"  hang  all  the  law  and  the  prophets  ?"  That  is, 
that  all  the  details  of  religion  and  morals,  are  but 
the  logical  unfoldings  of  this  simple  principle  ? 


CHAPTER  II. 

Section  I. — Conceptions. 

1.  In  unfolding  the  nature  of  Conceptions,  as 
also,  of  Judgment  and  Reasoning,  it  will  be  ne- 
cessary occasionally  to  repeat  a  few  things,  which 
were  unavoidably  introduced  by  way  of  anticipation 
in  our  brief  preliminary  exposition. 

2.  Conceptions  stand  contrasted  with  Intuitions, 
which     cognize     single     presentations,  „ 

°  o  x  /    Conception  and 

whether  external  or  internal,  whether  intuition  com- 
bodies   or  states  or   consciousness,  im- 
mediately   and    intuitively.      Conceptions,  on  the 
other    hand,  grasp   (con-capio)  a  plu- 
rality in  one,  through  the  medium  of  grasps  a  plural- 

i  i         i        ity  in  one. 

a    common    sign    or    mark,    whereby 
they    are,    so    far    forth,   represented.     This  plu- 
rality may  be  of  objects  thus  brought  to  This   plurality 

•  ,  i  may   be   either 

unity  in  a  common  genus,  by  a  common    „    , .    . 

J  o  7    J  of    objects     or 

mark   or    resembling    quality,    as   the  marks,  included 

under  a  common 

whole  class  of  red  things  are  brought  name. 

43 


44  LOGIC.  [Chap.  11. 

to  unity,  or  classified  by  the  common  mark  of  red- 
ness. Or  it  may  be  a  plurality  of  marks  or  attributes 
under  one  name.  As  hexagon  includes  the  two 
_  , ,       marks,  rectilineal  figure  and  six  sides. 

Expressed  by  a  7  & 

General  Word.    Another  aspect  of  the  same  truth  is, 

Conception  is  that  act  or  product  of  the  mind  which 

is  expressed  by  a  General  Word.     And  hence, 

3.   Conception  is  that  product  of  the  mind  which 

results  from  Generalization,  whereby  many 

Formal  Defini-  /  .  . 

tion  of  Concep-  individuals   are  combined  in  one  class, 

through  one  or  more  similar  qualities,  and 

are  indicated   by   a   common   term.     Thus,   certain 

pieces  of  iron-ore  are  observed  to  have  the  property 

of  attracting  iron,  and  are  generalized  into  one  class 

x     .         .,     under  the  name  Magnets.    It  is  obvious 

Involves     Ab-  ° 

straction.  that,  in  attending  to  this  quality  of  at- 

tracting iron,  exclusively  of  others,  there  is  a  with- 
drawing  or   abstracting   it   from   them.     Here   is 

Abstraction.  There  is  Comparison,  in 
ximparis  orc|er  to  detect  the  resemblance  of  these 

qualities  in  the  several  magnets.     Then  there  is  the 

Classification  or  Generalization  by  vir- 

Generalization.  p    ,i  •  n  -rv      n 

tue  of  this  resemblance,  finally,  in 
order  to  complete  and  guard  the  product  of  this 
process,  the  name  "  Magnet"  is  applied  to  this  class. 


Sec.  I.]  CONCEPTIONS.  45 

This  is  Denomination.     Thus  we  have  a  conception 

formed  as  the  result  of  Abstraction,  Corn- 
Denomination. 
parison,  Generalization,  Denomination. 

4.  Notion  is  a  term  of  wider  import  than  Con- 
ception.    It  is  used  almost  as  loosely  if0ti0n. 

as  Idea.      It   includes   representations  I(iea, 

not  only  of  Conception,  but  of  mental  similitudes  of 

objects  remembered  by  simple  Imagination. 

5.  Conceptions    and    the    corresponding    terms 
which  express  them,  may  be  viewed  either  as, 

Abstract, 

i.  e.  as  expressing  a  quality  irrespective  of  any  object 
in  which  it  inheres,  as  Magnetism,  Heat,  Atstract    Con 
Wisdom,  Virtue.  Or  they  may  be  viewed  ceptiona. 
as, 

Concrete, 

L  e.  as  inhering  in  some  object,  as  magnet,  hot-blood, 
wise  man,  virtuous  person.     These  dis- 

Concrete. 

tinctions  will  also  apply  to  the  inherence 
of  higher  in  lower  conceptions,  as  will  be  seen  when 
we  come  to  define  this  distinction.     They  also  pre- 
pare us  to  understand  the  distinction  between  Deno- 
tative, Connotative,  and  Xon-Connotative  terms. 


46  LOGIC.  [Chap.  II. 

6.  A  Term  is  Denotative  in  so  far  as  it  denotes 
an  object  or  objects.     All  names  of  single  objects, 

.  i.  e.  Singular  Terms,  have  this  capacity, 

Terms.  Singu-  whether  they  be  proper  names,  or  com- 
mon  terms  with  an  individualizing  par- 
ticle; as  "John,"  "this  man."  All  strictly  concrete 
terms,  as  fools,  stones,  trees,  have  this  capacity, 
besides  their  power  to  connote.  Abstract  concep- 
tions have  not  this  capacity.  They  include  quali- 
ties but  not  objects,  as  virtue,  color,  wisdom. 

7.  Connotative  (which  are  also  Attributive),  terms 
Connotative  or  conceptions  denote  objects,  and  con- 
Attnbutive.  n0^e  qualities  along  with  them,  as  men, 
roses,  animals.  Such  are  all  Adjectives,  inasmuch 
as  they  express  qualities  belonging  to  the  objects 
indicated  by  the  names  to  which  they  belong.  The 
Adjectives  foolish,  organized,  etc.,  can  only  be  used 
in  reference  to  their  appropriate  objects.  When, 
however,  adjectives  are  used  to  qualify  abstract 
nouns,  they  denote  not  so  much  objects,  as  the 
quality  which  they  still  further  determine.  Thus, 
"great  virtue,"  " scrupulous  veracity."  Of  course, 
all  concrete  common  nouns,  as  horses,  quadrupeds, 
etc.,  are  connotative.  They  denote  objects  and  con- 
note qualities. 


See.  II.]  CONCEPTIONS.  47 

8.  Non-connotative  words  are  proper  nouns 
which  denote  objects  simply;  also  ab-  Noa_0omiota_ 
stract  common  terms,  which  denote  qua-  tative. 
lities  (and  in  this  sense  have  denotative  power),  but 
connote  no  objects;  as  blackness,  harmony,  etc. 
Proper  names  ordinarily  denote  intuitions  or  single 
objects,  not  conceptions. 

9.  Proper  Names  sometimes  acquire  the  attributes 
of  common  terms,  when  the  individuals  „  >T 

7  Proper    Names 

they  denote  become  types  of  a  class,  become  com- 
As  when  we  speak  of  a  Webster,  a  Wash- 
ington, a  Napoleon,  or  of  the  Caesars  and  Nimrods 
of  our  race ;  i.  e.  the  class  of  men  who  have  the 
qualities  of  Caesar  or  Nimrod.  In  such  cases,  these 
names  are  connotative.  Adjectives  formed  from 
them  are  like  other  adjectives  in  this  respect,  as 
British  subjects,  a  Websterian  or  Johnsonian  style, 
i.  e.  a  style  having  the  qualities  of  the  style  of  these 
authors. 

Sect.  II. — Higher  and  Lower  Conceptions. 

10.  It  is  evident  that  the  same  process  of  gene- 
ralization may  be  applied  to  classes  as   Generalization 
to  individuals.     Thus  triangles,  squares,  °     c  assesind^ 
parallelograms,  polygons,  etc.,  may  all  viduals. 


48  LOGIC.  [Chap.  II. 

be  generalized  into  the  one  class  of  rectilinear 
figures.  Circles,  ellipses,  parabolas,  etc.,  may  be 
reduced  to  the  one  class,  curvilinear  figures.  Recti- 
linear and  curvilinear  again  may  be  united  as  one  in 
the  higher  genus,  plane  figure.  Dogs,  lions,  horses, 
etc.,  may  be  generalized  into  the  higher  class  of 
quadrupeds.  And  so  of  numberless  examples  which 
will  readily  occur  to  the  student.  Now  in  such 
cases,  the  broader  conception  which  includes  the 

Higher  and  low-   °therS>  is  Called  the  Higher-      The  liar" 

er  Conceptions.  r0wer  ones  which  are  included,  are  the 
Lower.  Quadruped  is  a  higher  conception  than 
dog  or  fox.  As  the  process  of  combining  lower 
conceptions  into  a  higher,  by  laying  aside  their  dif- 
ferences, is  Generalization ;  so  that  of  resolving  the 
higher  into  the  lower,  by  adding  on  these  differences, 
n.     .    ..       is  called  Determination.     The  Concep- 

Determmation  r 

of  Conceptions,  tion  triangle  undergoes  this  process  when 
it  is  resolved  or  determined  into  equilateral,  isosceles, 
and  scalene. 

11.  In  the  scale  of  higher  and  lower  Conceptions 
we   have    another    application   of  the 

Concrete      and 

Abstract     ap-  distinction  of  the  Concrete  and  the  Ab- 

plied  to  Classes.      ,  at^'i         n  j.*  i*  i.    • 

stract.     A  higher  Conception  which  is 

Abstract  when  taken  by  itself  alone,  becomes  Con- 


Sec.  III.]  CONCEPTIONS.  49 

crete  when  incorporated  with  another  in  a  lower 
Conception.  Thus  the  Conception  rationality  is 
Abstract,  when  taken  by  itself  alone,  but  when 
united  with  animality  it  becomes  Concrete  in  the 
lower  Conception  manhood. 

Sect.  III. — Genus,  Species,  Individual,  Differentia, 
Essence,  Accident,  Property. 

12.  In  any  series  of  higher  and  lower  Concep- 
tions, each  higher  is  a  Genus  to  those 

Genus. 

next  below  it,  out  of  which  it  is  formed 

by  generalization.      Those  next   below  it  are  its 

Species.   Thus  birds,  fishes,  beasts,  rep- 
Species. 
tiles,   men,  are   species   to   the   Genus 

animal.     Differentia,  or  Specific  Difference,  is  the 

mark   or   quality  which   distinguishes 

1  J  &  Differentia     or 

one  species  from  others  under  the  same  Specific  Differ- 
Genus.     Individual  or  Intuition  is  that  ence' 
which  is  logically  indivisible,  although  it  may  be 
capable  of  physical  division.     It  can- 

.  .         Individual. 

not,  therefore,  be  a  species,  although  it 
may  be  one  of  the  constituents  of  a  species.     An 
ox  cannot  be  divided  logically,  but  may  be  physi- 
cally into  hide,  horns,  quarters,  etc.     But  then  it  is 

no  longer  an  ox.     Of  course  then  an  individual  can 
5  d 


50  LOGIC.  [Chap.  II. 

never  be  a  Species  or  Genus,  which  is  always  com- 
.  „       posed  of  a  plurality  of  individuals.    Es- 

Essence  is  Gen-    x  x  ' 

us  and  Differ-  sence  refers  to  Species,  and  its  essential 
constituents,  i.  e.  its  Genus  and  Differ- 
entia. These  are  called  Essence,  because  when 
present  the  Species  is  present ;  if  either  be  absent 
Lo°ical  Defini-  that  ^s  wanting.  These  which  consti- 
tion*  tute  the  Essence  of  a  Species,  also  con- 

stitute Logical  or  Essential  Definition.  As  rose 
(Genus),  red  (Differentia),  constitute  the  Essence  or 
Definition   of  red-rose.     Accident,    or   Accidental 

Conception  belongs  to  a  part,  and  not 

Accidentt 

to  the  whole  of  a  class,  as  sickness  or 
health  to  man.  Property  belongs  to  the  whole  of 
a  Species,  but  is  not  a  part  of  its  Essence:  as  liability 
to  laugh,  or  grow  gray,  in  man  whose  Essence  is 
(Genus)  animal,  (Differentia)  rational.  Where  these 
are,  whatever  else  is  wanting,  there  is  manhood. 
Where  they,  or  either  of  them,  are  not,  there  man- 
hood is  not. 

Sect.  IV. — Subaltern  and  Proximate  Genera  and 
Species.    Summum  Genus  and  Infima  Species. 

13.  In  a  series  of  higher  and  lower  Conceptions,  it 
has  been  shown  that  the  same  one  may  be  a  Genus 
to  those  next  below,  and  Species  to  that  next  above. 


Sec.  IV.]  CONCEPTIONS.  51 

Those  Species  to  which  any  given  Species  becomes  a 
genus,  are  relatively  to  it  Subaltern  Subalter]1  Gen. 
Species.  Those  Genera  which  are  Species  ns  and  Species. 
of  a  higher  Genus  are  called  Subaltern  Genera. 
Thus  White-oak,  Yellow-oak,  Live-oak,  etc.,  are 
Subaltern  Species  to  oak,  which  is  a  Species  of  the 
genus  tree ;  and  is  therefore  a  Subaltern  Genus  to  it. 
Summum   Genus   is   that   highest  class  a  n 

&  Summum  Genus. 

which  is  never  a  species.     Infima  Species   ^fi^a  Species. 
is  that  lowest  class  which  is  never  a  Genus. 

14.  Proximate   Genera   and    Species   are   those 
which  are  next  to  each  other  in  order  of  Pr  xim  t  G 
ascent  or  descent.     Thus  triangle  is  the  era  and  Species. 
Genus  proximate  to  equilateral,  isosceles  and  scalene 
triangle.     They  are  proximate  Species  of  triangle. 

15.  It  should  be  noted  that  Summum  Genus  may 
be  Absolute,  with  reference  to  the  Uni- 

Absolute   Sum- 
Verse,  in    which   case   it   is    Thing   or  mum  Genus. 

t>  •  i  • ,  l      -r>   i   j.  •  Relative  also, 

hemg  simply ;  or  it  may  be  Kelative  to 

a   particular   department — as   animal  is  Summum 
Genus  of  corporeal  beings  having  life  and  conscious- 
ness :  plane  superficial  figure  with  re- 
ference   to    triangle,   Square,   etc.      And   Summum  Genus 

fe     '      ^  '  and  Infima  Spo- 

it  is  sometimes  fixed  arbitrarily  with  cies  often  arta- 

o  .      ,i  p  . .      trarily  fixed. 

reference  to  the  purposes  ot  some  parti- 


52  LOGIC.  [Chap.  II. 

cular  discussion.  Infima  Species  is  also  often  diffi- 
cult to  be  fixed,  for  it  is  often  hard  to  find  classes 
that  have  no  sub-classes.  It  might  be  supposed 
that  isosceles  triangle  was  Infima  Species  among 
plane  superficial  figures.  Yet  it  may  be  divided 
into  those  of  different  magnitudes :  and  each  of  these 
again  into  those  drawn  on  slates,  boards,  paper,  etc. 
This  therefore  is  seldom  reached  absolutely.  It  is 
rather  fixed  somewhat  arbitrarily  with  reference  to 
the  exigencies  of  the  inquiry  in  hand. 

16.  It  is  important  to  note  the  difference  between 
t    .   ,    j  >t     Species  in  Logic  and  in  Natural  History. 

Logical  and  Na-      r  °  J 

turai     Species  In  Logic,  as  has  been  shown,  it  means 

distinguished.  „    .  ,     ,  ,  .    . 

one  oi  the  proximate  lower  classes  into 
which  any  higher  class  or  genus  may  be  divided. 
The  same  class  may  thus  be  Genus  to  a  lower,  and 
Species  to  a  higher. 

In  Natural  History,  however,  Species  means  only 
such  a  class  of  animals  as  has,  or  might  have  de- 
scended from  a  single  pair,  and  the  varieties  of 
which  may  permanently  inter-propagate  among 
themselves.  These  sub-species  are  by 
the  Naturalists  rigidly  named  Varieties. 
Bull-dog,  terrier,  grey-hound,  etc.,  are  Varieties  of 
the  Species,  dog. 


Sec.  V.]  CONCEPTIONS.  53 

In  a  Logical  sense,  quadrupeds,  reptiles,  birds, 
fishes,  are  species  of  the  genus  animal.  In  the 
Naturalistic  sense,  though  they  include  Species,  they 
are  not  themselves  Species  at  all,  as  they  want  the 
marks  already  noted,  of  actual  or  possible  descent 
from  a  single  pair,  and  of  inter-propagation.  We 
are  aware  that  some  naturalists  adopt  other  criteria 
of  natural  species.  This,  however,  is  not  the  place 
for  extended  discussion  of  that  question. 

Sect.  V. — The  Three  Powers  of  Conception.     Exten- 
sion, Intension,  and  Denomination. 

17.  From  the  analysis  already  given  of  the  forma- 
tion of  Conceptions,  it  appears  that  they  Extension  of 
include  a  plurality  of  objects  through  Conceptions. 
their  resembling  qualities  indicated  by  a  common 
name,  and  that  the  number  of  objects  so  included, 
increases  with  the  height  of  the  Conception.  Thus 
man  includes  more  objects  than  poet,  orator,  philo- 
sopher ;  and  animal  more  than  man.  This  power 
to  denote  objects  constitutes  the  Extension  of  Con- 
ceptions. 

It   is   equally  plain   that   every  conception  in- 
cludes or  connotes  qualities  or  marks,  j^tcnaifln  or 
The  ground  of  classification  is  resem-  Comprehension. 
5  * 


54  LOGIC.  [Chap.  II. 

bling  qualities.     Therefore  the  conception  of  any 

class  involves  these  similar  qualities  or  marks  which 

constitute  it.     Thus  the  conception  square  involves 

the  following  marks :  1.  Rectilineal  figure :  2.  Having 

four  sides :  3.  And  those  sides  equal :  4.  And  its 

angles  right  angles.     The  conception  man  involves 

the  marks,  1.  Animal,  2.  Rational.     This  power 

of  conceptions  constitutes  their  Intension,  formerly 

called  their  Comprehension,  which  by  Whateley  has 

been  identified  with  Extension.* 

It  is  not  less  clear  that   conceptions  have  the 

capacity  to  receive  names,  and  must  re- 
Denomination,        .      ,,        .        -1,1  in 
ceive  them  in  order  to  be  preserved  and 

used.  A  conception  without  a  name,  is  like  an  un- 
fenced  crop,  or  a  volatile  odor.  This  is  the  power 
of  Denomination. 

To  these  three  powers  of  Conception,  three  im- 
portant processes  respectively  correspond,  viz. :  Divi- 
sion to  Extension ;  Definition  to  Intension ;  and 
Explanation  to  Naming  or  Denomination. 

*  See  Logic,  Harper's  Edition,  p.  152. 


Sec.  VI.]  CONCEPTIONS.  55 


Sect.  VI. — Inverse  Eatio  of  Extension  and  Intension, 

or  Comprehension. 

18.  As  the  Extension  of  Conceptions  increases, 
their   Intension  diminishes.     It  is  by    .      „  .     . 

J     As     Extension 

laying  aside  the  distinctive  marks  of  increases,    In- 

-,  ,.  ,,     ,  .  ,  .    ,  tension    dimin- 

lower  conceptions,  that  we  rise  to  higher,  ^Q3t 
that  is,  more  extensive  conceptions. 
Thus  by  laying  aside  the  distinctive  marks,  Equi- 
lateral, Isosceles,  and  Scalene,  we  arrive  at  the 
higher  conception,  Triangle,  which  has  greater  exten- 
sion, and  less  intension  than  isosceles,  or  scalene 
triangle.     So   poet,   orator,   statesman, 

,  ,  .  -,  .       .    .        .         ExampleSi 

have  less  extension  and  greater  intension 
than  man.  The  ratio  of  these  to  each  other,  there- 
fore, is  inverse.  Conceptions  then  may  be  regarded 
as  embracing  or  constituting  the  respective  wholes 
of  Extension  and  Intension,  each  of  which  decreases 
as  the  other  increases.  Of  course  in  Summum  Genus 
Extension  reaches  its  maximum,  and  Intension  its 
minimum ;  and  conversely  in  Infima  Species.    These 

wholes  have  sometimes  been  called  re- 
Logical  and  Me- 

spectively,  the  former  Logical,  the  latter  taphysical 
Metaphysical.   We  agree,  however,  with       ° e" 
Hamilton,  that  this  distinction  is  without  any  sum- 


56  LOGIC.  [Chap.  II. 

cient  ground,  each  alike  being,  in  one  aspect  Logical, 
and  in  another  Metaphysical.* 

Sect.  VII. — Denomination. 
19.  The  process  of  Denomination  keeps  pace  alike 
with  the  Extension  and  Intension  of 
Names  keep       Conceptions.     Thus,  as  the  extension  is 

pace  with   the 

Extension  and  increased,  names  are  employed  to  denote 

Intension       of  i  i  ji  -mi  i.    j_l. 

„       ..  each  enlarged  class,  till  we  reach  the 

Conceptions!  °  J 

highest,  which  is  Being  or  Thing.  And 
vice  versa;  as  we  add  on  successive  marks  to  Being, 
names  are  applied  to  include  or  connote  them,  till 
the  term  man  includes  being,  with  life,  sensation, 
and  reason.  All  this  is  well  illustrated  in  the  fol- 
lowing tabular  examples  from  Thomson's  Laws  of 
Thought,  which  we  copy,  because  it  is  hard  to  find 
or  invent  any  other,  in  all  respects  so  much  to  the 
purpose. 

*  Various  other  modes  of  expressing  this  double  capacity  of  a 

Conception  are  in  vogue.  Thus  a  Conception  viewed  as  an 

Extensive  Whole,  Intensive  Whole. 

has  has 

Extension,  Intension  or  Comprehension, 

Breadth,  Depth, 

Sphere,  Matter, 

Objects,  Marks, 

Power  to  Denote,  Power  to  Connote. 


Sec.  VII.] 


CONCEPTIONS. 


57 


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58  LOGIC.  [Chap.  II. 


Sect.  VIII. — Varieties  and  Characteristics  of  Concep- 
tions USUALLY  EXHIBITED  WITH  RESPECT  TO  THEIR  DE- 
NOMINATION, or  the  Names  which  Complete  and  Indi- 
cate them. 

20.  As  Conceptions  are  incomplete  till  they  are 
, ,  -    named,   and    these    names    are    called 

Various    kinds 

of  Terms  mark-  Terms,  or  Nouns,  so  certain  features  of 
ing  felturesn0f  Conceptions  are  usually  set  forth  as 
Conceptions.  belonging  to  these  terms  or  nouns. 
But  as  these  terms  stand  for  Conceptions,  so  the 
different  kinds  of  Terms  are  but  different  kinds  of 
Conceptions,  save  in  those  exceptional  cases  of 
proper  names,  in  which  they  denote  only  intuitions 
or  individuals. 

21.  The  first  division  of  nouns  is  into  Proper, 
Proper  Com-  Common,  and  Singular.  Proper  names 
rnon,  Singular,  denote  individuals  merely,  without  con- 
noting any  marks  or  qualities.  Common  names 
denote  conceptions,  and  the  objects  included  in  them, 
together  with  their  common  marks,  i.  e.  their  exten- 
sion and  intension.  Singular  terms  denote  single 
objects  by  means  of  a  common  noun,  having  its  sig- 
nification limited  by  an  individualizing  particle,  as 
this  man,  a  house,  some  animal. 


Sec.  VIII.]  CONCEPTIONS.  59 

22.  The  second  principal  division  of  nouns  is  into 
Attributive  and  Substantive.     Attribu- 

Attributive. 

tives  are  the  adjectives  of  Grammar. 
They  express  qualities  not  in  the  Abstract,  but  in 
the  Concrete,  as  belonging  to  some  substance.  They 
express  the  attributes  of  Nouns,  and  are  therefore 
used  only  in  connection  with  the  Nouns  of  which 
thev  are  ad j  uncts.  Substantive  Nouns  de- 

J  °  (  Substantive. 

note  objects  or  abstract  qualities,  to  which 
Attributives  may  be  applied.     Thus  tree  and  hard- 
ness are  Nouns  Substantive.    High  and  great  are  at- 
tributives which  may  be  respectively  ascribed  to  them. 

23.  Another  distinction  is  that  between  Distri- 
butive and  Collective  Nouns.     A  Noun 

Distributive, 

is  Distributive  or  used  distributively, 

when  it  is  applicable  to  each  and  every  individual 

included  under  it.     It  is  Collective,  or 

Collective. 

used  collectively,  when  it  is  applicable 
to  the  whole,  or  a  plurality  only,  but  not  to  each 
and  singular  of  the  objects  included  under  it.  Thus 
man  is  a  Distributive,  and  crowd  a  Collective  Noun. 
Soldier  is  a  Distributive,  army  a  Collective  Noun. 
The  same  noun  may,  however,  be  used  both  collec- 
tively and  distributively.  When  we  say,  "  these  trees 
are  oaks,"  trees  are  used  distributively.     When  we 


60  LOGIC.  [Chap.  II. 

say,  "these  trees  amply  shade  this  park/'  they  are  used 
Di  t  ib  ti  f  c°Hectively.  Hence  a  Term  is  said  to 
Terms.  be  Distributed,  when  it  is  so  used  as  to 

include  all  the  objects  signified  by  it  distributively ; 
that  is,  all  and  singular  of  them,  not  merely  a  part 
of  them,  nor  the  whole  of  them  collectively.  When 
we  say,  "all  men  are  mortal/'  men  is  Distributed. 
If  we  say,  "some  men  are  poets,"  men  is  not 
Distributed;  and  if  we  say  "all  men  number 
1,300,000,000/'  men  is  not  Distributed :  for  although 
all  men  are  spoken  of,  it  is  not  all  and  singular,  but 
all  taken  collectively,  that  are  meant. 

Terms  or  Conceptions  are  Absolute   and  Rela- 

Absolute  and    ^ve*     Absolute  are  irrespective  of  any 

Eelative.         other,  as  stone,  tree.    Relative  are  those 

which  imply  others.    As  son  implies  a  parent,  and 

king  a  subject.    A  pair  of  relatives  like 

Correlatives.       p  ,,  ,  n    i  ^         i    ,• 

father  and  son  are  called  Correlatives. 
In  all  Relative  Conceptions  there  is  a  ground  of 
Ground  of  Eela-  *ne   relation    (fitndamentum  rdationis). 
tlon'  In  the  case  of  king  and  subject,  it  is 

government.      In  that  of  father  and  son,  brother, 
sister,  etc.,  it  is  the  family.     Some  relatives  imply 
.  not  merely  one,  but  two,  or  even  several 

Cases  of  several  '  '  ' 

Correlatives.      Correlatives.     Thus,  cousin  implies  not 


Sec.  VIII.]  CONCEPTIONS.  61 

only  another  cousin,  but  parents,  one  of  whom  is 
brother  or  sister  of  one  of  the  parents  of  the  other 
cousin. 

24.  Contrary  and  Contradictory  Terms   or   Con- 
ceptions.    Contraries  are  the  most  op- 
posed that  can  possibly  belong  to  the 
same  subject,  as  wise  and  foolish,  soft  and  hard. 
Contradictories  are  simple  Negatives  of 

,        ,,  -.    .  ;1  .it      Contradictories. 

each  other,  and  between  them  include 
all  being  actual  and  possible.  Thus,  man  and  not 
man,  Ego  and  non-Ego,  are  pairs,  each  of  which 
comprises  the  universe,  not  only  of  actual,  but  of 
possible  being.  And  of  such  a  pair  of  Conceptions 
one  only  marks  out  any  definite  class  of  Definite  and  In- 
objects.  They  are  for  this  reason  called  defimte> 
Definite  and  Indefinite  Conceptions.  Of  the  two  Con- 
ceptions, man  and  not-man,  the  former  alone  contains 
any  thing  definite  or  positive  either  as  respects  ob- 
jects or  qualities.  The  latter  is  not  only  indefinite, 
but  essentially  infinite.  It  embraces  all  the  possi- 
bles but  man,  the  subtraction  of  which  does  not 
make  their  number  less  than  infinite,  ingnitated  Con- 
Hence  such  purely  Negative  Concep-  cePtioils' 
tions  are  sometimes  classed  by  logicians  as  Infini- 
tated  Conceptions. 

6 


62  LOGIC.  [Chap.  II. 

25.  It  is  not,  however,  true  of  most  Negative 
Most  Negatives  Conceptions,   that   in    their    real    and 

d°fi  Lta  J  In"  customaiT  signficance,  they  have  this 
finites.  infinity.     Especially  is  this  not  true  of 

Attributives.      Thus,  if  we  speak  of  unkindness, 
we  do  not  mean  every  thing  that  is  not  kind,  but 
we  mean  the  absence  of  this  quality  in  intelligent 
and  moral  beings  who  ought  to  be  kind,  and  in 
whom  to  be  unkind  is  to  be  harsh  or  severe.     Now 
a  conception  or  term  which  implies  the 
presence  of  any  mark  is  called  Positive, 
as  virtue,  wisdom,  benevolent.     A  term  which  im- 
plies the  absence  of  what  might  belong  to  a  given 
Privative.       subject,  is  Privative,  as  an  unkind  or 
Negative.       unholy  man.      Negative  terms  on  the 
other  hand,  deny  not  only  what  does  not,  but  what 
cannot  belong  to  some  given  object,  as  lifeless  stone, 
speechless  block.     These  do  not  belong  to  the  class 
of  Infinitated  Conceptions. 

26.  These  distinctions  are  not  without  practical 

importance.     In  the  first  place  they  add 

Importance    of 

these    Distinc-  to  our  variety  of  forms  of  thought  and 
expression,  and  so  to  the  means  of  pre- 
cision of  style.     The  words  unkind,   unholy,  un- 
learned, give  us  shades  of  thought  not  expressed  by 


Sec.  IX.]  CONCEPTIONS.  03 

the  words  harsh,  wicked,  ignorant.  Again,  the 
distinction  of  Privative  and  Positive  is  of  moment, 
in  reference  to  the  origin  of  evil  as  related  to  God. 
He  is  in  no  sense  the  cause  of  sin,  except  privatively 
or  negatively.  It  may  arise  from  the  absence,  not 
the  presence,  of  his  agency,  as  darkness  arises  not 
from  the  presence  but  the  absence  of  the  sun. 

27.  Two  terms  which  may  be  applied  to  the  same 
object  at  the  same  time,  are  called  Com-  n       , ., ,      , 

J  7  Compatible  and 

patible  or  Consistent,  as  red  and  round  Consistent. 
to  a  table;  diligent  and  healthy  to  man.     They  are 
Opposite  or  Inconsistent  when  they  can-    n 

rr  J  Opposite  and 

not   be  applied  simultaneously  to  the    Inconsistent. 
same   object,  as  "round   square   figure,"   "lifeless 
breathing  man." 

28.  The  important  distinctions  of  Abstract  and 
Concrete,  Connotative  and  Non-connotative  terms, 
were  sufficiently  explained  when  treating  of  the  cor- 
responding conceptions.  To  these  the  student  can 
recur,  chap.  II.,  sect.  I.  5,  and  II.  11. 

Sect.  IX. — Quality  of  Conceptions. 

29.  By  the  Quality  of  Conceptions  is  meant  the 
degree  of  perfection  with  which   they 
represent  to  the  mind  the  objects  and  ceptions defined. 


(J4  LOGIC.  [Chap.  II. 

the  marks  included  in  them.  In  this  regard,  Con- 
ceptions, like  all  cognitions,  are  perfect  in  proportion 
Tm.      '  as  they  have  the  several  virtues  of  Clear- 

Wnen  they  are  •> 

Perfect.  ness,  Distinctness,  and  Adequacy.     In 

proportion  as  they  have  the  opposite  vices,  they  are 
respectively  Obscure,  Confused,  and  Inadequate. 
The  nature  of  these  respective  virtues  and  faults  we 
will  now  proceed  to  explain. 

30.  A  conception  or  other  cognition  is  Clear, 
ci  a  Ob  wnen  ft  is  simply  distinguishable  from 
scare.  others,  and   Obscure  when   it   is   not. 

Thus  in  twilight  we  often  see  objects,  but  are  unable 
to  distinguish  them  from  each  other.  Our  cogni- 
tions of  them  are  obscure.  As  the  light  gradually 
comes  upon  them,  our  view  becomes  so  clear  that 
we  can  distinguish  them  apart.  The  uninstructed 
cannot  distinguish  Logic  from  Psychology  and  Me- 
taphysics, or  a  Court  of  Chancery  from  a  Court  of 
Law.  These  are  Obscure  conceptions  to  those  un- 
versed in  such  matters.  All  persons  are  afflicted 
with  more  or  less  of  this  obscurity  of  knowledge  in 
departments  to  which  they  have  not  given  special 
attention. 

31.  But  we  may  know  objects  or  conceptions,  so 
as  to  distinguish  them  from  each  other,  without 


Sec.  IX.]  CONCEPTIONS.  65 

being  able  to  point  out  the  marks  by  which  they 
are  so  distinguished.     Such  knowledge 

.     .        Distinct  and 

may  be  sure  as  far  as  it  goes.     But  it  is    confused  Cog- 
confused  with  respect  to  the  marks  or    mtlons  ex_ 

plained. 

differential  features  of  the  object.  This  is 
among  the  most  common  phenomena  of  our  intelli- 
gence. How  common  to  know  persons  of  our  acquain- 
tance from  each  other,  without  being  able  to  specify 
the  peculiarities  of  form  or  feature  which  distin- 
guish them  severally.     How  common  to 

,  ,,ii         i         •  j  •  c  t  r-n  Illustrations. 

be  sure  as  to  the  hand-writing  oi  diner- 
ent  persons,  without  being  able  accurately  to  define 
the  peculiarities  of  each.  How  often  do  lawyers  in 
court  perplex  witnesses,  and  torture  out  of  them 
absurd  answers,  by  asking  them  the  marks  by  which 
they  identify  the  persons  or  the  hand-writing  in 
regard  to  which  they  testify.  Yet  what  tribunal 
ever  discredited  a  witness  on  account  of  any  puzzle 
or  inconsistency  into  which  he  was  thus  drawn? 
Those,  however,  who  have  made  such  subjects  a 
study,  are  able  to  give  the  marks  of  difference. 
Their  knowledge  is  distinct,  while  the  other  is  con- 
fused. The  same  distinction  holds  in  regard  to  our 
understanding  of  conceptions.  If  we  take  the  con- 
ceptions mineral,  plant,  animal,  man,  how  few  who 
6*  B 


66  LOGIC.  [Chap.  II. 

do  not  surely  know  the  one  from  the  other  ?  But 
how  few  can  accurately  give  the  marks  which  dis- 
tinguish them  respectively  from  each  other?  A 
Clear  cognition  or  conception  then  knows  its  objects 
__  .    ,       _   from   other  objects.     An  Obscure   one 

Distinction   of  u 

Distinct    and    does  not.     A  Distinct  cognition  or  con- 
ception not  only  knows  its  objects,  but 
the  marks  of  those  objects.     A  Confused  one  knows 
its  objects  without  knowing  their  marks. 

32.  This  Distinctness  of  our  conceptions  may  be 
Ad  ate  d  both  Adequate  and  Inadequate.  It  is 
Inadeqnate.  Adequate  when  it  not  only  apprehends 
their  marks,  but  the  marks  of  these  marks.  And 
when  it  fails  of  this,  it  is  Inadequate.  Thus  we 
have  a  Clear  knowledge  of  the  conception  man,  when 
we  discriminate  it  from  animal,  plant,  etc.  We  have 
a  Distinct  knowledge  of  it,  when  we  know  its  marks 
to  be  animality  and  rationality.  This  knowledge  is 
Adequate  when  we  can  give  not  only  these  marks 
of  manhood,  but  can  also  give  the  marks  or  defini- 
tions of  animality  and  rationality,  those  of  the  former 
being  life  and  sensation,  of  the  latter  the  intuition 
of  supersensual  truths  and  the  power  of  thinking  in 
the  light  of  these  truths.  This  process  of  giving 
the  marks  of  marks  is  in  itself  capable  of  indefinite 


Sec.  X.]  CONCEPTIONS. 


67 


extension.     That  measure  of  it  which  is  adequate, 
cannot   be  decided  by  any  unvarying:  «    tt 

'  J  J      °    No    Unvarying 

rule.     It  varies  with  the  exigencies  and  Bales  of  Ade- 
requirenients  of  each  particular  discus-  quacy" 
sion,  and  must  often  be  determined  somewhat  arbi- 
trarily. 

Sect.  X— Notative  and  Symbolical  Conceptions. 

33.  This  is  a  pregnant   distinction.      A  Nota- 
tive Conception  is  such  that  when  pre-  Notative  Coi] 
sented  to  the  mind,  it  suggests  its  own  ception. 
marks  (notce)  by  its  very  name,  so  that  they  are  at 
once  and  indubitably  evident,  e.  g.  quadruped,  tri- 
angle, octagon,  oligarchy.     A  Symbol-     SymMical 
ical  Conception  is  one  which  serves  as  a     Conception. 
symbol   of  a  number  of  marks  or   characteristics 
which  it  does  not,  of  itself,  bring  before  the  mind 
using  it.     It  is  used  as  a  substitute  for,  or  represen- 
tative of,  the  marks  which  the  mind  does  not  stop 
to  bring  in  detail  before  itself,  and,  indeed,  which, 
in  many  cases,  it  could  not,  if  it  would.     Such  are 
the  conceptions  or  terms,  church,   family,  senate, 
philosophy,  etc.     Few  bring  before  their  minds  all 
the  marks    involved  in  these  conceptions.     Most 
persons  could  not  do  it,  who,  nevertheless  always 


68  LOGIC.  [Chap.  II. 

use  them  with  substantial  accuracy.     All  concep- 
tions which  are  used  without  an  apprehension  of 
their  marks  or  definition,  are  used  Symbolically. 
34.  All  Thorough  Knowledge  is  obtained  by  re- 
moving: from  our  conceptions  the  several 

Thorough  &  r 

Knowledge  how  imperfections  of  Obscurity,  Confusion 

obtained.  ,    T       -,  ,     -,        ,  , 

and  Inadequacy,  and  developing  these 
into  Clearness,  Distinctness,  Adequacy  and  Particu- 
larity;  as  also  by  unfolding  the  marks  of  Symbolical 
Conceptions  till  they  have  something  of  the  distinct- 
ness of  Notative  Conceptions.  This  is  no  less  essen- 
tial to  invention  and  style  in  Rhetoric,  than  to 
logical  thinking. 

It  is  accomplished  by  two  great  processes,  each 
of  which  must  be  pursued  in  proportion  as  we  would 
make  our  conceptions  clear,  distinct,  and  adequate. 

The  first  of  these  is  Logical  Division,  which  un- 
folds the  Extension  of  Conceptions. 

The  second  is  Definition,  which  unfolds  their  In- 
tension. 

These  processes  are  now  to  be  considered. 


Sec.  XI.]  CONCEPTIONS.  69 

Sect.  XI. — Logical  Division. 

35.  Logical  Division  divides  a  Genus  according 
to  its  extension,  i.e.  into  its  constituent  T    .   ,    -,>.  . 

7  Logical    Divis- 

and  proximate  Species.     It  may  then  ion  Defined. 
take  any  of  these  proximate  Species  for  a  Genus,  and 
divide  that  into  sub-Species.     In  like  manner  it  may 
divide  any  of  these  again,  and  so  on,  until  we  pass 
through  Infima  Species  to  individuals. 

36.  The  Genus  divided  as  being  the  higher,  is 
sometimes    called    the   Super-ordinate.  0  ,. 

1  Super-ordinate 

The  proximate  species  into  which  it  is  Genus. 
divided,   are   called   Co-ordinates.     If     Co-ordinate 
either  of  these  be  divided  into  parts  or      pecies' 
Species,  with  reference  to  its  superior  Genus,  it  is 
called  Subordinate  Genus.     Any  one  of    subordinate 
given  Co-ordinate  Species,  is  called,  in     Genus. 
relation  to  any  one  part  of  a  higher  or  lower  Co- 
ordinate Division  under  the  Summum     Disparate 
Genus,  Disparate.     Thus,  quadruped  is     Species. 
super-ordinate  to  lions,  leopards,  horses,     ExampieSi 
cats,   etc.     They  are   co-ordinate  with 
each  other.     They  are   subordinate  to  quadruped 
and  animal,  while  lion,  as  compared  to  fish,  Shet- 
land pony,  or  bull-dog,  is  Disparate. 


7Q  LOGIC.  [Chap.  II. 

37.  The  rules  for  correct  Logical  Division  are : 

a.  It  must  proceed  from  Proximate  Genera  to 

Proximate  Species,  and  not  per  saltum, 

Proximate  Ge-  or  arbitrarily.     To  Divide  animals  at 
nera  to  Proxi-  ouce  int0  whales,  sturgeon,  etc.,  without 

mate  Species,  .  . 

previously  dividing   them   into    birds, 
fishes,  ^Ui.,  would  be  a  violation  of  this  rule. 

b.  There  must  be  but  one  principle  of  Division, 
B  ne  princi-  fandamentum  divisionis.  In  dividing  a 
pie  of  Division,  library,  for  example,  it  will  not  do  to 
divide  the  books  according  to  price  and  according 
to  binding,  at  the  same  time.  To  do  this  is  to  vio- 
late the 

c.  Third  Eule,  which  is,  that  the  Divisions  must 

Divisions  Hutu-  be  mutually  exclusive.  They  must  not 
ally  Exclusive.    run  jn^0  eacn  other  by  cross-divisions. 

This  will  result  from  adopting  more  than  one  prin- 
ciple of  Division.  Thus  if  we  divide  the  books  of 
a  library  according  to  their  subject-matter,  and  ac- 
cording to  the  language  in  which  they  are  written, 
some  books  of  poetry,  history,  and  oratory,  will  be 
in  Latin,  French,  English,  etc.  One  fruitful  source 
of  perplexity  and  confusion  in  the  discussion  of 
subjects  is  unobserved  cross-divisions,  which  ought 
rigorously  to  be  avoided. 


Sec.  XL]  CONCEPTIONS.  71 

d.  All  the  parts  should  be  exactly  equal  to  the 
genus  divided ;  any  one  part,  and  the  gmn  of  partB 
sum  of  any  number  of  parts  less  than  e1uals  Drrisum. 
all,  should  be  less  than  the  Divisum  or  genus 
divided.  To  divide  mankind  into  rational  ani- 
mals and  all  others,  or  into  Europeans,  Asiatics, 
Americans,  and  Greenlanders,  would  be  a  violation 
of  this,  as  well  as  of  other  rules. 

e.  It  must  not  be  a  priori,  or  by  Infinitation. 
For  this,  although  in  form  regular  and 

Not  a  priori. 

exhaustive,  is  in  fact  useless.  It  adds 
nothing  to  our  knowledge.  To  divide  animals  into 
partridges  and  all  others,  or  partridges  and  not- 
partridges,  is  indeed  a  formally  complete,  but  a 
completely  useless  Division.  Such  a  Division  into 
two  members,  which  inevitably  are  contradictories, 
is  called  a  Dichotomy.  A  division  in  three  mem- 
bers is  called  a  Trichotomy :  into  many  members,  a 
Polytomy. 

38.  Physical  Division  or  Partition. — Logical 
Division  must  be  clearly  distinguished  from  Physi- 
cal Division  or  Partition.     The  latter 
divides  an  individual,  which  is  logically  logically  divisi- 
indivisible,  into  its  component  parts,  as 
a  ship  into  hull,  masts,  sails,  etc.     The  test  of  this 


LL 


2  LOGIC.  [Chap.  II. 


sort  of  Division  is  that  the  Divisum  cannot  be 
predicated  of  parts.  In  Logical  Division  it  always 
may.  We  cannot  predicate  ship  of  sails,  masts, 
etc.,  but  we  can  predicate  it  of  steamship,  sailing- 
ship,  etc. 

It  should  be  further  observed,  that  we  may  arbi- 
trarily make  collective  wholes  logical  individuals, 
when  it  suits  the  end  in  view.      Thus 

Collective 

Wholes  Logical  nations,  armies,  regiments,  etc.,  may  be 

Individuals.  ,  i  -r        •      i    •     v    •  i      i  r\n 

treated  as  Logical  individuals.  Uiten 
like  literal  individuals  they  cannot  be  so  divided 
that  the  divisum  can  be  predicated  of  the  parts. 
Thus  army  cannot  be  predicated  of  regiments,  nor 
regiments  of  companies,  nor  nations  of  towns. 

39.  The  thorough  logical  division  of  any  subject, 
Uses  of  Divis-  thus  defining  the  sphere  and  the  objects 
ion'  it  includes,  greatly  assists  the  clear,  tho- 

rough, and  facile  discussion  of  it.  It  also  aids  in- 
vention. The  most  sterile  mind  will  find  some- 
thing to  say  on  a  subject  well  mapped  out.  Indeed 
so  to  map  it  out,  is  to  say  something  important. 
Division  gives  clearness  to  our  Conceptions  by 
pointing  out  their  objects.  But  to  gain  distinctness 
and  adequacy,  we  must  resort  to 


Sec.  XII.]  CONCEPTIONS.  73 

Sect.  XII.    Definition. 
40.  This  gives  the  marks  of  Conceptions,  and 
unfolds  their  Intension.   It  thus  bounds    Definition  de- 
them  off  from  all  other  Conceptions,  so    scribed, 
that  we  not   only  know  that   they  differ,  but   in 
what  way  they  differ.    The  rules  for  correct  defini- 
tion are, 

a.  It  must  be  by  essential  marks.  The  essential 
marks  of  a  species  are  what  constitute  B  essential 
its  essence,  i.  e.  its  genus  or  matter,  and  Marks- 
differentia  or  form.  This  is  normal,  logical  defini- 
tion, or  definition  strictly  so-called.  All  other 
definition  is  valid  in  proportion  as  it  approximates 
to  tins. 

HHP"*  Let  not  the  student  forget  when  ashed  what  is 
logical  or  essential  definition,  that  it  is  ^^i  Defmi- 
made  up  of  the  genus  and   differentia.    tion' 

b.  It  must  include  the  objects  covered  by  the 
definitum,  or  species  defined,  neither  ^ot  too  Broad 
more  nor  less.  If  it  include  more,  it  is  nor  Harrow, 
too  broad.  Thus  to  define  a  whale  as  a  fish,  is  too 
broad.  To  define  a  fish  as  a  whale  is  too  narrow. 
A  definition  too  broad  is  detected  by  simple  conver- 
sion.   If  it  is  a  good  definition  of  a  whale  to  say  that 

7 


74  LOGIC.  [Chap.  II. 

it  is  a  fish,  then  all  fish  are  whales.     A  definition 
too  narrow  is  detected  by  conversion  by 

How  Detectedi  .  ...  ,-m  . P  ..    ■.  , 

contraposition,  lnus,  it  it  be  a  good 
definition  of  a  fish,  that  it  is  a  whale,  then  whatsoever 
is  not  a  whale  is  not  a  fish.  For  the  fuller  under- 
standing of  this,  the  student  must  recur  to  it  after 
studying  the  subject  of  conversion,  in  its  proper 
place,  under  the  head  of  Reasoning. 

c.  It  must  not  be  by  Negatives,  if  this  can  be 
Not  by  N  avoided.  Negatives  show  what  are 
tives.  n0^  instead  of  what  are  marks,  and  so 

add  little  to  our  knowledge.  To  define  man,  as 
not  an  angel,  or  not  a  brute,  is  unsatisfactory.  It 
does  not  tell  what  he  is.  There  are,  however,  Nega- 
tive words  and  conceptions,  which  in  "their  very 
nature  require  a  negative  definition,  as  unholy  is 
simply  not  holy. 

d.  It  must  not  be  in  vague,  ambiguous,  or  sense- 
Must  be  in  dear  less  language.  To  say  that  "truth  is 
Language.  ^he  grand  scope  of  all  existence/'  or 
that  "  beauty  is  the  harmony  of  being,"  are  exam- 
ples in  point. 

e.  It  must  not  be  Tautological,  i.  e.  through  the 
w     m      ,       word  defined,  or  any  of  its  derivatives,  or 

Not  Tautolo-  '  J  9 

gical.  synonyms  from  other  tongues,  or  the 


Sec.  XII.]  CONCEPTIONS.  75 

negative  of  its  opposites.  To  define  life  as  the  vital 
force,  or  the  state  of  living,  or  the  opposite  of  death, 
is  thus  to  err.  This  is  definition  in  a  circle,  cireulus 
in  definiendo,  for  such  definitions  return  upon  them- 
selves. If  light  be  defined  as  "  that  which  illumi- 
nates," per  contra,  "that  which  illuminates  is  light." 
The  circle  in  definition  as  in  argument,  is  often  un- 
observed. How  easy  to  define  a  plank  as  a  thick 
board,  and  a  board  as  a  thin  plank? 

/.  It   must   be   Precise   and   free   from   surplus 
words.      These  surplus  words,  though 

0      Precise  and  free 

true,  may  convey  a  false  implication,  from  Surpius- 
To  say  that  a  parallelogram  is  a  rectili-  age' 
neal  four-sided  figure,  whose  opposite  sides  are 
parallel  and  equal,  is  to  state  the  truth.  But  the 
words  "and  equal,"  are  unnecessary  to  the  definition : 
and  they  convey  this  false  implication  that  there 
may  be  such  figures  whose  opposite  sides  are  parallel, 
but  not  equal.  This  vice  is  of  more  frequent  occur- 
rence in  ordinary  thought  and  speech,  than  in  formal 
definition.  How  natural  to  say,  "  we  ought  not  to 
calumniate  so  good  a  man,"  as  if  it  were  right  to 
calumniate  anybody  ? 

41.  Absolute  Summum  Genus  cannot  be  logically 


76  LOGIC.  [Chap.  Li 

defined,  because  it  has  no  differentia.     Thus,  being 
can  only   be   defined    by  some    synonym    or    de- 
scription casually  substituted  for  it.    It 

Absolute   Sum-  ,       -,    P       ,  ,,.  . ,     .      ,  .   , 

mum  Genus  uot  ma7  be  defined  as  a  thing,  or  that  which 

Logically  Defi-  has  existence.     Summum  Genus  in  any 

nable. 

particular  sphere,  being  such  only  rela- 
tively, and  always  a  species  of  a  higher  genus,  is  of 
course  capable  of  strict  logical  definition. 

42.  Simple  Ideas  are  incapable  of  logical  defini- 

Simplo  ideas  tion>  as  they  cannot  be  analyzed  into 
likewise.  elements,  and  therefore  are  without 
genus  and  differentia.  They  can  only  be  defined 
like  Summum  Genus,  by  synonymous  or  descrip- 
tive equivalents.  Red  is  a  color.  This  is  genus. 
But  who  can  give  the  differentia,  that  separates  it 
from  other  colors  ?  What  is  color  ?  What  is  good- 
ness or  beauty  ?  What  is  the  respective  genus  and 
differentia  of  each  ?  But  although  not  definable,  do 
they  need  defining  ?  Are  they  not  self-evident  and 
plainer  in  themselves  than  any  definition  could 
make  them? 

43.  Logical  definition,  strictly  considered,  refers 
only  to  Species,  and  therefore  does  not  technically 

apply   to   Individuals.       Hence   other 

Individuals, 

how  Defined.      methods  of  defining  them  have  been  de- 


Sec.  XII.]  CONCEPTIONS.  77 

vised.  They  may  be  defined  by  the  intuition  of 
them,  through  the  senses  if  they  be  bodies,  or 
through  the  light  of  consciousness,  if  they  be  men- 
tal states.  Or  they  may  be  defined  by  some  pecu- 
liar and  inseparable  Accidents,  as  a  virtual  Differ- 
entia.  Thus,  Cicero  might  be  defined  as  "the 
greatest  Roman  Orator,"  and  the  first  Napoleon  as 
"  the  greatest  French  General."  They  are,  however, 
thus  defined  by  all  that  is  essential  in  a  logical  defi- 
nition. They  are  referred  to  the  Infima  Species 
under  which  they  fall,  and  discriminated  from  other 
individuals  under  it,  by  some  mark  peculiar  to  them- 
selves. Thus  Washington  may  be  defined  as  "  the 
first  President  of  the  United  States."  Here  the 
Infima  Species,  President  of  the  United  States,  is 
to  the  individuals  under  it,  what  every  proximate 
genus  is  to  its  co-ordinate  species.  This  then  may 
be  taken  as  the  genus,  and  " first"  as  the  dif- 
ferentia. 

44.  Indeed,  in  all  definition,  whether  of  indi- 
viduals or  species,  the  genus  and  differ-  Qenus  ana  £if. 
entia  may  be  considered  as  two  com-  ferent^a  really 

J  two    Commum- 

municant  genera,   and  the  Conception  cant  Genera. 
defined  that  which   is  included  within  the  sphere 
of  their   coincidence.     Either   raav  be   considered 


78  LOGIC.  [Chap.  II. 

genus  and  the  other  differentia,  and  vice  versa,  at 
convenience.  Thus,  if  we  define  a  man  as  a  rational 
animal,  this  extends  over  so  much  of  the  concep- 
tions, rational  and  animal,  as  overlap  each  other. 
Thus : 


In  like  manner,  so  much  of  the  genera,  "  Presidents 
of  the  United  States,"  and  "  fourth,"  as  overlap 
each  other,  are  just  equal  to,  and  define  James 
Madison,  fourth  President  of  the  United  States. 

45.  As  there  are  many  cases  in  which  a  strictly 
Methods  of  De-  l°gical  definition  is  either  impracticable 
finition.  or  inconvenient,  several  other  methods 

of  defining  are  occasionally  adopted,  which  serve 
more  or  less  effectually  to  clear  the  definitum,  and 
to  bound  it  off  from  all  else.  Including  these,  the 
methods  of  definition  in  all  amount  to  six,  arranged 
by  logicians  as  follows  : 

a.  Resolution.  This  resolves  the  Conception  into 
Resolution,      its  marks,  genus  and  differentia,  and  is, 


Sec.  XIL]  CONCEPTIONS.  79 

as  we  have  seen,  the  standard,  normal,  logical,  essen- 
tial definition.     Thus,  "  man  is  a  rational  animal." 

b.  Composition.      This  is  the  reverse  of  resolu- 
tion, and   unites   the   marks   into  the 

r*  ,.  r.      ,  .   t     ,,  ,         Composition. 

Conception  ot  which  they  are  concrete 
parts.      Thus,  "  a  rational  animal  is  man." 

c.  Division:  i.  e.  according  to  extension,  into  its 
constituent  parts,  whether  species  or  in- 
dividuals.    Thus,  "the  New  England 

States  are  Maine,  New  Hampshire,  Vermont,  Mas- 
sachusetts, Connecticut,  and  Rhode  Island."  "  The 
animal  kingdom  consists  of  Radiates,  Mollusks,  Ar- 
ticulates, and  Vertebrates." 

d.  By   Colligation,  the  reverse  of  the  last,  i.  e. 
uniting  the  constituent  parts  acccording 

to  extension  together,  as  James,  John, 
Matthew,  Thomas,  etc.,  were  the  twelve  Apostles. 
The  Earth,  Mars,  Mercury,  Venus,  etc.,  are   the 
Planets.    This  formula  furnishes  the  minor  premise 
for  the  Inductive  Syllogism. 

e.  By  the  substitution  of  Symbols  or     Exchange  of 
names ;  as  "  religion  is  piety."  Symbols. 

/.  By  Casual   Substitution  of  narrative   or  de- 
scriptive  phrases,  as,  wisdom  leads  to 

Casual  Substi- 

virtue  and  happiness.     This  last,  how-   tution. 


80  LOGIC.  [Chap.  II. 

ever,  hardly  conies  up  to  the  exactness  required  in 
real  definition.  Nor  should  the  fifth  method  be 
used  when  it  can  be  avoided. 

46.  Most  logicians  refer  to  the  distinction  be- 
tween Nominal  and  Heal  Definition,  and.  strangely 
Nominal  and  inconsistent  accounts  have  been  given 
real  Definition.  0f  [^  These  terms  are  adapted  to  mis- 
lead. Nominal  Definition  is  the  Definition  of  a 
name ;  Real,  of  a  thing.  But  the  Definition  of  a 
name  is  none  the  less  a  Real  Definition.  Indeed, 
all  strictly  Logical  Definitions  are  of  names,  and 
give  the  marks  which  these  names  stand  for.  That 
is,  they  give  the  marks  connoted  by  these  names. 
This  is  the  proper,  normal  province  of  Definition. 
As  to  qualities  of  things  not  connoted  by  the  name, 
they  are  important,  and  belong  to  scientific  investi- 
gation and  the  increase  of  our  knowledge,  but  do 
not  directly  constitute  Definition.  They  may  afford 
the  means  of  correcting  or  improving  the  accepted 
Definition  of  these  names,  which  is  Definition  pro- 
per. In  Mathematics  and  the  Ideal  and  Formal 
Sciences,  the  Definition  of  the  Name,  is  of  necessity 
the  Definition  of  the  Thing.  The  Definition  of  the 
names,  "  Circle,"  "  Conception,"  "  Extension/'  "  In- 


Sec.  XII.]  CONCEPTIONS.  81 

tension,"  etc.,  is,  of  course,  the  Definition  of  the 
thing. 

47.  From  this  analysis,  it  appears  that  Definition, 
or  the  distinct  explication  of  the  marks  imp0rtance  of 
of  conceptions,  is  of  fundamental  im-  Defillitlon' 
portance  in  thinking,  investigating,  and  discoursing. 
An  accurate  Definition,  or  presentation  of  the  status 
questio7iis,  will  often  settle  controversies  otherwise 
interminable.  Without  such  Definition,  all  discus- 
sion and  investigation  must  be  futile  and  unsatis- 
factory. And  it  is  quite  as  powerful  a  stimulus  to 
invention  as  Logical  Division. 

48.  It  is,  moreover,  quite  plain  that  Definition 
and  Division  are  mutual  helps  to  each  •.      ,  , 

Definition    and 

other.     When  we  Divide  a  Genus  into  Division  mntnai 

.,  ,  •  n  •»        aids. 

its  proximate  species,  we,  oi  necessity, 
are  bringing  to  light  the  differences  between  those 
species.  These,  with  the  Genus,  make  up  the  Defi- 
nition. On  the  other  hand,  looking  for  the  differ- 
ences, we,  of  course,  are  finding  the  boundaries  of 
the  several  species  into  which  Division  separates  the 
genus. 

F 


CHAPTER    III. 

JUDGMENT. 

Section  I.    Its  Constituent  Parts. 

1.  Judgment  is  that  act  of  the  mind  which,  upon 
Judgment  de-    comparing  two  Conceptions,  or  an  in- 
fined,  dividual  object  of  intuition  with  a  Con- 
ception, affirms  that  they  agree  or  disagree ;  that  they 
do  or  do  not  belong  to  each  other.     Thus,  "Vic- 
toria is  queen."     "Angels  are  not  men."     A  Judg- 
ment expressed  in  words  is  a  Proposi- 

Proposition.       , .  T    -.  .  -.  ^ 

tion.  Judgments  and  Propositions  are 
always  either  true  or  false.  No  other  form  of 
thought  or  expression  has  these  attributes. 

2.  Strictly  speaking,  as   has   been   already  ob- 

served, in  the  last  analysis,  every  intel- 

Strictly  every  7  J  J 

Mental  Act  a    ligent  act  is  a  Judgment.     To  know  is 

to  discriminate,  and  therefore  to  judge. 

Even  feeling  and  sensation,  the  most  rudimental  form 

82 


See.  I.]  JUDGMENT.  83 

of  consciousness,  involves  a  knowledge  and  so  a 
Judgment  that  it  exists.  This  is  Primitive  as 
distinguished  from  Logical  Judgment.  Primitive  Judg- 
And  yet  it  is  hard  to  maintain  this  dis-  ment' 
tinction  without  qualification.  For  the  most  Primi- 
tive Judgment  affirms  that  something  is  predicates  ex- 
or  is  not;  i.  e.  it  affirms  that  the  Concep-  istence  op- 
tion, Existence,  agrees  with  some  individual  sub- 
ject. But  beyond  the  mere  predication  of  Existence, 
Primitive  Judgments  do  not  go.  Logi-  Logical  Judg. 
cal  Judgments  are  founded  on  Concep-  ments- 
tions  formed  by  Abstraction  and  Generalization  from 
these  Primitive  Judgments.  Yet,  since  Primitive 
Judgments  involve  the  Conception  of  Existence, 
which  withal  is  Summum  Genus,  the  two  flow  into 
each  other. 

3.  And  it  is  to  be  observed,  that  all  the  processes 
of  Thought,  whether  by  Conceptions,     _ 

to     '  J  r  ?   All  Thought 

Judgments,  or   Reasonings,  in  reality  resolvahie  into 

,     p,  -,    ,  •       ,      •       t     i        Judgments. 

proceed  from  and  terminate  in  Judg- 
ments. Conception  is  the  product  of  the  Judgments 
involved  in  abstraction  and  generalization,  whereby 
many  objects,  through  some  common  mark  or  point 
of  similitude,  are  grasped  together.  Conception  fixes 
and  preserves  this  Judgment,  by  a  common  name. 


84  LOGIC.  [Chap.  III. 

Thus,  the  conception  and  the  name,  bi-ped,  is  the 
fruit  and  confirmatory  sign  of  the  Judgment,  that 
animals,  which  agree  in  having  two  feet,  may  be  put 
in  a  class  denoted  by  the  common  name,  biped.  As 
Conception  is  the  product  of  a  Judg- 

Conceptions  ,  ...  , .      .     ,    ,  T     , 

formed  and  ex-  ment>  so  xt  1S  explicated  by  a  Judg- 
piicated  by        ment.     Thus  "  bi-peds  are  two-footed 

Judgments.  t  #  .  „ 

animals."     "Animals    are    conscious. 
They  interpen-  Jn  short,  Conception  and  Judgment  in- 

etrate   each 

other.  terpenetrate  each  other.     In  one  view, 

Conception  is  a  certain  stage  of  Judg- 
ment.     Judgment   in   form  develops  Conception. 
Reasoning,  too,  the  third  great  process 

Seasoning  also 

is  by  Judg-      or    form  of  thought,  deals  only  with 

Judgments,  and  their  relations  to  each 
other,  as  will  be  seen,  when  we  come  to  treat  of  it. 
It  proceeds  from  one  or  more  Judgments  given  to 
others   founded    upon    them.      Thus,    in    the   last 

analysis,  Logic   being   the   Science   of 

Logic  the  Sci-  . 

ence  of  Judg-  Thought  is  the  Science  01  Judgments, 
ments*  into  which  all  thought  is  finally  resol- 

vable. Nevertheless  it  is  convenient  to  treat  of 
pure  formal  Judgment  by  itself,  after  Conception 
which  furnishes  the  materials  of  Judgments ;  and 
before  Reasoning,  which  is  composed  of  them,  and 


Sec.  L]  JUDGMENT.  85 

in  concluding  that  one  Judgment  flows  from  others, 
forms  the  Judgment  that  it  does  so. 

4.  Judgment  being  thus  a  mental  affirmation  of 
the  agreement  or  disagreement  of  two  notions,  one 
of   which    at   least    is   a    Conception,  Terms    0f     a 
these  two  notions  are  called  the  terms  Judsmenti 
{termini,  extremes)  of  the  Judgment. 

That  which  is  spoken  of  is  the  Subject  of  the 
Judgment.     That  which  is  affirmed  or  guweot|  pre(ji- 
denied  of  the  other  is  called  the  Predi-  cate' 
cate.     That  which  connects  the  two  is  M    ,    , 

Copula  is  verb 

the  Copula.     This  is  always  the  verb  "to  be  "in  pres- 
to be,  in  the  Present  Tense  Indicative, 
if  the  Judgment  be  affirmative :  and  the  same  with 
the  negative  particle  affixed,  if  the  Judgment  be 
negative.     Thus : 

Sub.  Cop.    Pred. 


The  earth    is  round. 

Sub.  Cop.  Pred. 

Oaks 


are  not 


pines. 


The  Copula,  in  many  cases,  is  not  directly  ex- 
pressed by  the  word  is,  or  is  not,  but  is  copula  often  im- 
in  other  phrase,  which  implies  them.  Plled< 
When  any  other  than  the  Substantive  verb  is  em- 
ployed as  Predicate  it  includes  the  Copula.     Thus, 


86  LOGIC.  [Chap.  III. 

Sub.  Cop.      Prert. 

"  he  runs,"  is  equivalent  to,  he  is  running.    iC  No  men 

Sub. 


are  sinless/'  is  the  same  as  to  say  of  all  men   that 

Cop.  Pred. 


they  are  not]  sinless. 

When  Existence  simply  is  expressed,  the  verb 
Predicate  when  to  be  is  both  Predicate  and  Copula ;  as, 

,  Sub.  Pred.  Cop. 

implied.  God  ig  =  ig  exigting> 

5.  When  any  mood  or  tense  of  the  verb,  except 
m      ,  ,         the  present  indicative  in  the  Copula,  is 

What  belongs  x  x        ' 

to  the  Predi-    significant,  this  significance  belongs  to 

the  Predicate  and  not  to  the  Copula. 

Thus,  if  we  say,  "  This  farm  was  fertile,  whether  it 

be  so  now  or  not,"  it  is  the  same  as  to  say,  this  farm 

Pred. 


IS 


one  formerly  fertile  .    The  weather  may  be  good, 

Pred. 


the  weather  is  what  may  be  good|.  As  either  term 
of  a  Judgment  may  be  a  Conception  including  differ- 
ent objects,  or  having  several  marks,  so  several  words 
may  be  employed  to  make  up  a  term.    Thus,  |"  The 

Sub.  Cop.  Pred. 


}} 


dews  of  the  evening    are  |the  tears  of  the  sky. 
"  Birds,  fishes,  beasts,  and  reptiles,  are  animals." 

6.  Words  which  alone  cannot  express  conceptions, 
Categorematic     or  intuitions,  cannot  of  themselves  con- 

and  Syncatego- 

rematio  Words,    stitute  terms  of  a  Judgment.     They  can 


Sec.  III.]  JUDGMENT.  87 

only  enter  into  these  terms  by  combination  with 
verbs  and  nouns  substantive  and  adjective.  Such 
are  articles,  prepositions,  conjunctions  and  adverbs. 
These  are  Syncategorematic;  nouns,  adjectives,  and 
verbs,  on  the  other  hand,  are  Categorematic,  because 
they  can  of  themselves  be  Terms. 

Sect.  II. — Quantity,  Quality,  Eelation,  and  Modality 

of  Judgments. 

7.  Judgments   may   be   viewed,    I. 

Judgments     in 

With  reference  to  the  relation  of  the  respect  of  Quan- 
predicate  to  the  extension  of  the  sub-  tlty" 
j  ect — Quantity. 

II.  With  respect  to  the  relation  of  the  predi- 
cate to  the  intension  of  the  subject — 

Quality.  *""* 

III.  With  respect  to  the  manner  of  connecting  the 
predicate  with  the  subject — Relation.         Relation. 

IV.  With  respect  to  the  degree  and  kind  of  cer- 
tainty in  the  connection  of  subject  and 
predicate — Modality. 

Sect.  III. — Quantity  op  Judgments. 

8.  With  respect  to  Quantity,  Judgments  are  either 
Universal,     Particular,    or     Singular. 

'  &  Universal 

Judgments  are  Universal  when  the  Pre-     Judgments. 


83  LOGIC.  [Chap.  III. 

dicate  is  affirmed  or  denied  of  all  the  Subject  taken 
distributively,  as,  "  all  men  are  sinners  ;"  "  no  men 
are  angels." 

Judgments  are  Particular  when  the  Predicate  is 
affirmed  or  denied  of  an  indefinite  part  of  the  sub- 
ject, as,  "some  men  are  orators;"  "some 

Particular,        ^  -^  .     „ 

(jrovernments  are  not  Democratic. 
Judgments  are  Singular ;  a.  when  the  Predicate 

is  affirmed  or  denied  of  individuals,  as, 

"  Caesar  was  a  Conqueror ;"  "this  man 
is  not  learned."  b.  When  the  subject  is  a  plurality 
of  individuals  taken  collectively.  A  collective  noun 
is,  for  Logical  purposes,  Singular:  as,  "This  crowd 
is  tumultuous,"  "An  army  consists  of  soldiers." 
9.  Singular  Judgments,  for  all  Logical  purposes, 

may  be  accounted  as  Universals,  since 

mente^'eq^va'    in  them>  the  whole  Subject  is  Spoken  of, 

lent  to  Univer-   an(J    t}iey    are    subject    to    the    laws    of 
sals. 

Universals. 

In  like  manner,  when  any  Definite  part  of  the 

Subject  is  taken,  it  may  be  considered 

Also  a  Definite  J  . 

part  of  the  Snb-  as  a  universal.     For  the  whole  class 
jec '  denoted  by  the  subject-name  with  its 

limiting  adjuncts  is  spoken  of — Thus  "  these  men  are 
natives  of  Ireland." 


Sec.  IV.]  JUDGMENT.  £9 

It  is  in  place  here  to  add,  that  Judgments  are 
further  distinguished  as  Simple  and  Compound. 
Judgments  are  Simple  when,  in  fact  as  well  as  form, 
there  is  but  one  subject  and  one  Predicate,  as,  "  men 
are  rational  animals."     A  Judgment  is     „.    , 

°  Simple  and 

Compound  when,  though  simple  in  form,  Compound 
by  a  plurality  of  subjects  or  predicates,  u  gmen  s' 
there  is  in  force  and  effect  a  plurality  of  Judgments. 
Thus,  "  Peter,  James,  and  Thomas  were  Apostles,' ' 
amounts  to  three  propositions,  one  affirming  of  Peter, 
another  of  James,  and  another  of  John,  that  he  was 
an  Apostle.  "  Men  are  rational,  accountable  and  im- 
mortal," may  be  divided  into  three  propositions,  each 
having  "men"  for  the  subject,  but  one  having  the 
predicate  *  rational,"  the  other  "  accountable,"  etc. 

Sect.  IV. — Quality  of  Judgments. 
10.  The  differential  Quality  of  a  Judgment  is 
that  it  affirms  or  denies  the  agreement  of 
Subject  and  Predicate.    Hence  in  respect  Affirmation   or 
of  Quality,  Judgments  are  either  Affir-  Negati<m' 
mative  or  Negative.     jggsf0  Let  the  learner  remember 
that  the  Logical  Quality  of  a  Judgment  refers  to  its 
being  Affirmative  or  Negative.     The  truth  or  falsity 
of  a  Judgment  is  of  course  of  supreme  importance. 

8* 


90  LOGIC.  [Chap.  III. 

But  this  pertains  to  its  matter,  not  to  its  form,  with 
which  alone  formal  Logic  concerns  itself. 

11.  A  Proposition  is  Affirmative  or  Negative,  ac- 
cording as  it  has  not  or  has,  a  negative  Copula; 
Quality  in  the  * e'  when,  whatever  be  the  form  of  ex- 
Copula,  pression,  the  real  force  of  a  negative 
does  not  or  does,  fall  on  the  Copula.  Thus,  "no 
iron  is  silver/'  is  negative,  for  it  asserts 
of  all  iron  that  it  is  not  silver.  "  A  per- 
son not  vicious  is  virtuous,"  is  affirmative,  because 
the  force  of  the  negative  does  not  fall  on  the  Copula 
but  on  one  of  the  terms.  "A  few  men  are  wise,"  is 
affirmative ;  "  but  few  men  are  wise,"  is  in  reality  ne- 
gative, for  it  is  equivalent  to  "  most  men  are  not  wise." 

Judgments  then  as  to  Quantity  and  Quality,  as 
The  four  Logi-  thus  unfolded   by   the   old   Logicians, 

cal    Judgments  r  1  •  1     ji         i  1 

and  th  ir  s  are  *our>  which,  they  nave  been  accus- 
als, tomed  to  mark  by  the  Symbols,  A.  E. 
I.  O.,  as  follows : 

Universal  Affirmative,  ....  A. 

Universal  Negative, E. 

Particular  Affirmative,  ....  I. 
Particular  Negative,      .     .     .     .0.* 

*  The  additional  Judgments  recognized  by  recent  Logicians 
will  be  noticed  in  due  time. 


Sec.  VI.]  JUDGMENT.  91 

Sect.  V. — Distribution  of  Terms  in  Judgments. 

12.  Of  the  foregoing  Judgments  all  Universals 
and  no  Particulars  distribute  the  Subject. 

All  Negatives  and  no  Affirmatives  tribute  the  Snb- 
distribute  the  Predicate.  Jectl  Negatives 

the  Predicate. 

The  reason  of  the  first  rule  is  obvious, 
for  in  Universals  the  whole  subject  is  spoken  of 
Distributively.*     In  Particulars  only  a  part  of  it. 

No  Negative  Judgment  can  hold  good  unless  it 
cuts  off  the  whole  of  the  Predicate  from  the  subject. 
Thus,  if  we  say,  "  some  men  are  not  poets,"  the 
whole  of  the  class  of  poets  is  cut  off  from  these  "some 
men."  "  No  men  are  perfect,"  cuts  off  the  whole  of 
the  class  "  perfect "  from  the  class  men. 

Sect.  VI.— Eelation  of  Judgments. 

13.  The  Relation  of  Judgments  has  respect  to  the 

manner  of  the  connection  between  the 

Relation  either 

subject  and  Predicate.     In  this  respect  Categorical    or 
Judgments    are   either   Categorical   or     ypo 
Hypothetical. 

*  Collective  Nouns  are  no  real  Exception,  since  in  a  Logical 
sense,  they  are  individuals  and  form  the  subjects  of  Singular 
Judgments. 


92  LOGIC.  [Chap.  III. 

14.  A  Categorical  Judgment  asserts  or  denies  the 

agreement  between  the  subject  and  Pre- 
dicate, simply  and  unconditionally,  as, 
"  Brutus  killed  Caesar,"  "  a  traitor  is  not  a  patriot." 

15.  A  Hypothetical  Judgment  asserts  or  denies 

such  agreement  upon  a  condition,  viz : 
ypo   e  of  the  truth  or  falsity  of  some  other 

Judgment.  Thus,  "if  crops  are  large,  food  is 
cheap."     "  This  man  is  either  holy  or  unholy." 

'.  ,     „       16.  Hypothetical  Judgments  are  of 

Three  kinds  of  Jr  & 

Hypothetical      three  kinds :  Conditional,  Disjunctive, 

Judgments.  i  -rv«i  j* 

and  JDilemmatic. 

17.  The  Conditional  Judgment  affirms  such  a 
Conditional  region  between  two  others,  respec- 
Jndgments.      tively   called   Antecedent   and  Conse- 

Antecedent  and   <IUent>  that>  if  the   former   be   trUe>  the 

Consequent,  latter  is  true  also,  as,  "if  the  sun 
shines,  it  will  give  heat."  Conditionals  are  indi- 
cated by  the  particles,  "if,"  or  its  equivalents, 
"  when,"  "  in  case  of,"  etc. 

18.  The  conditional,  like  all  hypothetical,  has 

in  it  a  categorical  element,  i.  e.  it  asserts 

Hypothetical 

have  a  Categori-  categorically  a  certain  relation  between 

the  Antecedent  and  Consequent ;  such, 

that,  if  the  former  is  true,  the  latter  is  true ;  and  if 


See.  VI.]  JUDGMENT.  93 

the  latter  is  false  the  former  is  false.    It  often  ex- 
presses the  relation  of  cause  and  effect.  m      _  _  ,  ^ 

x  Causal  Relation 

If  the  cause  operates  the  effect  will  fol-  often  in  Condi- 
low.    It  is  to  be  observed  that  a  condi- 
tional does  not  assert  the  truth  of  either  of  its  mem- 
bers, but  of  the  relation  between  them. 

7  Do    not    assert 

It  may  assert,  not  only  a  causal  rela-  the  truth  of 

..  1     ,    ,1  ,i         r.  ,    •  either  member. 

tion,  but  the  truth  of  a  certain  argu- 
ment.   Thus,  u  if  drunkards  drink  what  intoxicates, 
A.  B.  drinks  what  intoxicates."     This 

.         ,         .       Other  relations. 

is  not  an  assertion  either  that  drunk- 
ards, or  A.  B.  drink  what  intoxicates ;  nor  that  the 
former  is  the  cause  of  the  latter ;  but  that  there  is 
such  a  relation  between  the  two,  that  if  the  former 
be  true  the  latter  is  true.  A  certain  fact,  however, 
is  by  implication  asserted  as  the  foundation  of  this 
relation,  viz.,  that  A.  B.  is  a  drunkard. 

19.  Disjunctive  Judgments  assert  the  connection 
between  the  predicate  and  the  subject,  _.  .     x. 

L  or    Disjunctives  as- 

with   an  alternative   indicated  by  the  sert  with  an  ai- 

•  i  .i  i  m,  // ..    •     ternative. 

particles,  either  and  or.     lhus,  "it  is 
either  Spring,  Summer,  Autumn,  or  Winter."     The 
force  of  it  is  that  if  one  member  be  affirmed,  all  the 
others  are  denied.     If  one  is  denied,  then  some  one 
of  the  residue  is  true.     This  is  founded  on  the  law 


94  LOGIC.  [Chap.  III. 

of  Excluded  Middle.     A  judgment  or  its  contra- 
.p     ,  ,     -n     dictory  must  be  true,  and  there  is  no 

Founded  on  Ex-  J  7 

eluded  Middle,    middle  between  them.     So  conditionals 
are  founded  on  the  law  of  Sufficient 

Its       members 

mutually  exciu-  Reason.     Of  categoricals  the   affirma- 
tives are  founded  on  the  principle  of 
Identity,  and  the  negatives  on  the  law  of  Contradic- 
tion. 

20.  Hence,  in  order  to  any  valid  conclusion  from 
the  affirmation  or  denial  of  either  member  of  a  dis- 
junction, these  members  must  be  mutually  exclusive. 
Indeed  such  alone  are  genuine  disjunctives.  Dis- 
Differ  from  Par-  junctives  must  not  be  confounded  with 
titives.  Partitive  Judgments,  which,  under  the 

form  of  a  disjunctive,  simply  predicate  of  a  genus 
its  several  species ;  as,  "all  Africans  are  either  bond 
or  free."  This  is  but  dividing  the  genus  into  its 
component  parts  or  species.  It  differs  from  the  dis- 
junctive in  this,  that  the  predicates  are  affirmed 
concurrently,  and  not  alternatively,  of  the  subject. 
The  affirmation  of  the  one  is  not,  as  in  a  pure  dis- 
junctive, a  denial  of  the  other,  although  the  predi- 
cates are  still  mutually  exclusive  with  regard  to  the 
portions  of  the  subject  to  which  they  respectively 
belong. 


Sec.  VII.]  JUDGMENT.  95 

21.  Dilemmatic  Judgments  involve  a  combina- 
tion of  the  conditional  and  disjunctive.  Dilemmatic 
Thus,  "  if  A.  B.  succeeds,  he  will  either  Judgments. 
rule  or  ruin."  Here  the  disjunction  is  in  the  conse- 
quent of  the  conditional.  It  may  also  be  in  the 
antecedent.  "  If  man  is  either  good  or  ill  deserving, 
he  is  a  moral  agent." 


Sect.  VII. — Substitutive  Judgments. 
22.  Substitutive  Judgments  are  those  which  being 
affirmative  have  a  distributed  predicate,     g^stitntives 
This  distribution  of  the  predicate  can-     defined. 
not  be  known  from  the  mere  form  of  expression. 
As  we  have  already  seen,  affirmatives  as  such,  do 
not  distribute  the  predicate.     To  say  that  men  are 
mortals,  is  merely  saying  that  they  are  in  the  class 
of  mortals.     They  in  fact  comprise  a 
part  but  not  the  whole  of  mortals.     But 
if  we  say,  "  men  are  rational  animals,"  we  mean  all 
rational  animals,  for  there  are  none  but  men.     This, 
however,  does  not  appear  from  the  affirmative  form 
of  expression,  any  more  than,  if  we  were  to  say, 
"  men  are  animals."     We  know  it  from  other  evi- 
dence.    "Rational  animals"  is  the  definition   of 


96  LOGIC.  [Chap.  Ill, 

men,  and  is,  therefore,  co-extensive  with  it.     In  all 

All  Definition  cases  °f  Definition  then,  and  in  all  the 
Substitutive.  kinds  of  Definition  which  have  been 
pointed  out,  we  have  Substitutive  Judgments. 

23.  Judgments  of  this  kind  are  called  Substitu- 
Wh  called  *^ve'  because  the  predicate  may  be  sub- 
Substitntive.  stituted  for  the  subject  without  limiting 
the  quantity,  either  of  the  j  udgment,  or  of  the  predicate 
substituted.  If  we  define  men  to  be  rational  ani- 
mals, we  can  sav  that  "all  rational  animals  are 
men."  If  we  say  that  "Maine,  New  Hampshire, 
etc.,  are  the  New  England  States,"  we  can,  by  sim- 
ple substitution,  say  that  "  the  New  England  States 
are  Maine,  New  Hampshire,  etc." 

24.  Substitutive  Judgments  are  either  Particular 
„    .       or  Universal.     Of  these  latter  we  have 

Eitber  Particu- 
lar or  Univer-  already  given  examples.     The  former 

are  such  as,  "  some  stars  are  planets,"  i.  e. 

all  the  planets:  "some  men  are  poets,"  i.  e.  all  poets. 

25.  Affirmative  Judgments,  in  which  the  predi- 
Attributive  cate  1S  undistributed,  are  called  Attri- 
Judgments.  butive,  because  they  affirm  an  attribute 
of  the  subject,  without  taking  this  attribute  in  its 
whole  extent,  or  substantively.  Thus,  "  men  are 
rational." 


Sec.  VII.]  JUDGMENT.  97 

26.  The  importance  of  Substitutive  Judgments 
will  appear,  when  we  come  to  treat  of 

the  subject  of  reasoning.     They  render  Substitutive 
many    processes    of    reasoning    valid,  Judsmeilts' 
which  would  otherwise  be  invalid,  owing  to  the  non- 
distribution  of  affirmative  predicates,  as  will  be  ex- 
plained in  the  proper  place. 

27.  The  reason  why  logicians  who  have  recog- 
nized this  class  of  judgments,  have  why  this  per- 
treated  this  subject  as  belonging  to  the  ***  VtT" 

J  &     fe  lation  of  Judg- 

Relation  of  judgments,  or  as  concerned  merits. 
with  a  peculiar  class  of  them,  in  respect  to  the  man- 
ner of  the  connection  of  the  subject  and  predicate, 
is,  that  it  exhibits  the  quantity  of  the  predicate  as 
related  to  the  subject.  Indeed  every  affirmative 
judgment,  when  fully  explicated  in  language,  be- 
comes an  equation  of  the  subject  and  predicate  as  to 
quantity,  and  so  a  Substitutive  Judgment.  This 
will  appear  if  we  explicitly  quantify  EqnationofSuI). 
the  predicate,  i.  e.  fully  express  in  words  ject  and  Predi- 
what  we  mean  in  thought.  Thus,  if 
we  say,  "  all  men  are  mortals,"  we  mean,  "  they 
are  (i.  e.  =)  some  mortals."  "  All  men  are  rational 
animals/'  means  "  all  men  are  (i.  e.  =)  all  rational 

animals." 

9  G 


98  LOGIC.  [Chap.  Ill, 

28.  Substitutive  Judgments  are  indicated  respec- 
tively, the  universals  by  the  letter  U,  and  the  par- 
ticulars by  the  letter  Y.     Thus,  we  have 

The    Symbols 

of  Substitutive    six  different  kinds  of  judgments,  desig- 

Judgments.  ,     ^      ^  ±.\     '  l  r.    i 

nated  by  their  several  symbols  as 
follows : 

Universal  Attributive,  ....  A. 
Particular  Attributive,  ....  I. 
Universal  Negative,  .  .  .  .  E. 
Particular  Negative,  .  .  .  .  O. 
Universal  Substitutive,  .  .  .  U. 
Particular  Substitutive,      .     .     .  Y. 

29.  [Besides  these,  Sir  William  Hamilton  has 

lx.    undertaken  to  develop  two  others  ;  viz., 

Negatives  with  x  7  7 

undistributed     Universal     and     Particular     Negative 

PredicateSi  T     ,  .  •,-!  .•  ,    »i     ,    i  *■ 

Judgments  with  undistributed  predi- 
cates, which  he  marks  by  the  respective  symbols  tj 
and  w.  But  undistributed  negative  predicates  are 
so  contrary  to  all  normal  thought  and  language, 
that,  at  best,  they  are  useless,  and  need  not  claim 
our  attention.    The  Judgments,  "  No  men  are  some 

animals,"  "  and  some  men  are  not  some 

Insignificant 

and  worthless,     animals,"  are   awkward,   insignificant, 


Sec.  VIII.]  JUDGMENT.  99 

and  worthless,  being  nearly,  if  not  quite  incapable 
of  real  contradiction.*] 

Sect.  VIII. — Analytic  and  Synthetic  Judgments. 

30.  Analytic  Judgments  are  those  in  which  the 
predicate  is  involved  in  the  very  Con-  Analytic  Judg- 
ception  or  Definition  of  the  subject.   As,  ments- 
"  man  is  rational."     "  Quadrupeds  are  four-footed." 

*  They  carmot,  with  slight  exception,  be  opposed  by  contrary 
or  contradictory  propositions,  in  any  normal  use  of  language. 

The  following  table  in  which  A  stands  for  a  distributed,  and  I 
for  an  undistributed  term,  and  the  letters  f  and  n  respectively 
for  an  affirmative  or  negative  copula,  exhibits  at  a  glance  the 
import  and  force  of  the  Eight  Judgments  recognized  by  Hamilton. 

A.  Afi.  All  are  some.  All  men  are  mortals. 

E.  Ana.  Not  any  is  any.  No  men  are  angels. 

I.  Ifi.  Some  are  some.  Some  trees  are  beautiful. 

0.  Ina.  Some  are  not  any.  Some  coins  are  not  silver. 

U.  Afa.  All  are  all.  All  men  are  all  rational  animals. 

Y.  Ifa.  Some  are  all.  Some  men  are  all  the  poets. 

77.  Ani.  Not  any  are  some.  No  planets  are  some  stars. 

g>.  Ini.  Some  are  not  some.  Some  trees  are  not  some  oaks. 

a  is  without  force  because  not  contradictory  to  nor  inconsistent 
with  any  other  proposition.  >j  may  indeed  have  greater  force.  But 
this  is  seldom  important  in  actual  thought.  Both  judgments  in- 
deed are  rather  conceivable  than  actual  in  normal  thought,  and 
for  practical  purposes,  without  assertory  force. 


100  LOGIC.  [Chap.  III. 

They  therefore  require  no  proof.  They  are  evident 
simply  from  the  analysis  of  the  subject.  Hence 
they  are  a  priori,  i.  e.  known  from  the  conditions 
given,  if  not  always  in  the  most  absolute  meaning 
of  a  priori,  yet  from  the  definition  of  the  subject. 

31.  Synthetic  Judgments  are  those  in  which  the 
Synthetic  Judg-  predicate  adds  to  the  conception  or  defi- 
meats.  nition  of  the  subject.     They,  therefore, 

require  proof.  Thus :  "  laurel- water  is  poisonous," 
"horned  animals  are  ruminant,"  "the  conception 
of  a  perfect  being  involves  his  existence."  Synthetic 
Judgments  are,  with  a  qualification  to 
t,  be   noted,  a    posteriori.     The    Formal 

Exception  in  f         Mr 

Formal  Sci-       Sciences,  and   those  which   deal   with 

ences. 

necessary  truth,  furnish  us  a  peculiar 
class  of  Judgments  that  are  both  synthetic  and  a 
„      ,       .     priori.     All  the  demonstrated  proposi- 

How  they  give  ±  x      x 

Synthetic  Judg-  tions  in  Geometry,  e.  g.  are  a  priori. 
Yet  they  are  not  a  part  of  the  definition. 
They  are  not  immediately  suggested  or  implied  by 
it.  They  require  to  be  proved  by  a  chain  of  reason- 
ing from  the  definitions,  more  or  less  extended. 
Yet  this  reasoning  is  a  priori.  The  same  is  true  of 
most  of  the  principles  of  Logic.  In  this  sense  we  have 
Synthetic  Judgments  a  priori.     They  are,  in  truth 


Sec.  IX.]  JUDGMENT.  101 

partly  analytic,  in  that  they  are  ultimately  evolved 
from  the  definitions ;  synthetic  in  that  they  require 
proof  beyond  the  mere  statement  of  the  definition. 
The  origin  of  this  use  of  the  terms  analytic  (avaloco, 
to  take  asunder),  and  synthetic  (oovridyfii,  to  put 
together),  is  evident  from  their  etymology. 

The  terms  Explicative  and  Ampliative  have,  for 
obvious  reasons,  been  employed  to  de-  Ex  u   .. 
note  the  same  properties  of  Judgments  Ampliative. 
as  Analytic  and  Synthetic. 

Sect.  IX.— The  Modality  of  Judgments. 

32.  The  Modality  of  Judgments  respects  the  pos- 
sibility, certainty,  or  necessity  of  the  The  Modality  of 
connection  of  the   predicate  with   the  **»*  *>; 

*  longs  to  Applied 

subject.  This,  however,  really  belongs  L°sic- 
to  the  meaning  of  the  predicate  rather  than  to  the 
copula,  or  any  part  of  the  logical  form  of  the  judg- 
ment. Strictly,  therefore,  it  pertains  to  the  matter 
rather  than  the  form  of  the  judgment,  to  Metaphy- 
sics instead  of  Logic.  It  belongs,  accordingly, 
rather  to  applied  than  to  pure  Logic.  To  this  we 
shall  therefore  defer  it,  although  it  is  sometimes 
treated  at  this  point. 


9* 


102  LOGIC.  [Chap.  III. 

Sect.  X. — Plueative  Judgments. 

33.  Plurative   Judgments    are    those    in   which 

Plurative  Judg-   more  tnan  ^alf,  but  not  all  of  the  Sub- 
menu defined.    jec£  [s  taken  ;  as,  "  Most  men  are  vain." 
Of  a  similar  nature  are  Numerically  Definite  Judg- 
ments, i.  e.  those  in  which  a  definite 

Numerically 

Definite  Judg-    number  or  numerical  proportion  of  the 

ments.  i  .         •         ■> 

subject  is  taken. 
Both  of  the  foregoing  have  some  importance  as 
giving  rise  to  a  peculiar  kind  of  valid  syllogism 
which  will  be  explained  in  its  proper  place.     See 
chap.  V.,  sect.  I.  5. 

Sect.  XI. — Conversion  of  Hypotheticals  into  Catego- 

RICALS. 

34.  It   has   already  been   shown   that  in  every 
_      .    .   ,      Hypothetical  Judgment  there  is  a  cate- 

Hypotheticals  J  L  ° 

have  a  Cate-     gorical  element,  which  affirms  or  de- 

gorical  element.       .       , ,         .  ,  . ,     . .     ,       ,    , .        , 

nies  the  given  hypothetical  relation  be- 
tween certain  categorical  judgments.  This  being  so, 
by  a  slight  change  of  phrase,  they  may  be  made 
Categorical  in  form.  This  can  be  done,  as  follows, 
a.  Conditionals  may  be  so  converted  by  substi- 
Conditionals       tilting  for  the  particles  "  if,"  "  when," 

how  turned  into 

Categoricais.      etc.,  which    have  a  conditional   force, 


Sec.  XL]  JUDGMENT.  103 

such  phrases  as  "the  case  of,"  the  "circumstances 
in  which/'  etc.  Thus  the  conditional,  if  A  is  B, 
X  is  Y,  is  the  equivalent  of,  "  the  case  of  A  be- 
ing B  is  the  case  of  X  being  Y,"  which  is  a 
categorical.  The  conditional,  "  if  the  thermometer 
is  at  zero,  ice  forms  rapidly,"  may  be  transformed 
into,  "  the  case  of  the  thermometer  being  at  zero," 
or  "the  case,"  or  "the  circumstance,"  or  "the 
time  in  which  the  thermometer  is  at  zero,  is  that  in 
which  ice  forms  rapidly." 

Certain  Abbreviations  are  practicable  when  the 
same  terms  are  found  in  both  antece- 

,.        Abbreviations 

dent  and  consequent.  Thus  the  condi-  in  the  case 
tional,    "if  Peter   is   a   drunkard,    he     of  only  tbree 

7  Terms. 

(Peter)  is  degraded,"  is  equivalent  to 

"  every  drunkard  is  degraded,"  otherwise  it  could 

not  be  true. 

b.  Disjunctives  may  be  turned  into  Categoricals 
by  using  all  their  members  for  one  of 

,      .  •  ,.  .,  ,         Disjunctives. 

the  terms,  and   the   phrase,  "possible 

cases,"  or  the  like,  for  the  other,  thus  forming  a 

judgment  by  Colligation,  which,  as  we 

.  „  _       .     ,    By  Colligation. 

have  seen,  is  the  opposite  ot  .Logical 

Division.     Thus:   "This  season  is  either  Spring, 


1Q4  LOGIC.  [Chap.  III. 

Summer,  Autumn,  or  Winter,"  is  equivalent  to 
either  of  the  categoricals,  "the  possible  cases  in 
regard  to  this  season,"  or  "  the  only  alternatives  in 
regard  to  it,  are  Spring,  Summer,  Autumn,  Win- 
ter." 

As  has  been  shown  before  also,  Disjunctives  may 
„    „      ,  .      be  turned  into  Conditionals,  by  taking; 

By  first  being  '     J  & 

turned  into  Con-  the  contradictory  of  one  of  their  mem- 
bers for  the  antecedent,  to  which  the 
other  members  become  consequents.  Thus,  in  the 
foregoing  example,  "  if  it  is  not  Spring,  it  is  either 
Summer,"  etc.  When  once  a  conditional,  it  can  be 
made  a  categorical,  according  to  the  rules  already 
given,  e.  g.  "  The  case  of  its  not  being  Spring,  is 
the  case,"  etc. 

c.  Dilemmatic  Judgments  being  compounded  of 
Conditionals  and  Disjunctives,  may  be 

Dilemmatic 

Judgments  to  be  resolved  into  these,  and  each  of  these 

Eesolved.  ,  ,  1    .    .  ,  1 

may  be  changed  into  categoricals,  ac- 
cording to  the  methods  just  indicated.  Thus,  the 
Dilemmatic  Judgment,  "  If  iEschines  did  or  did 
not  join  in  the  public  rejoicings,  he  was  either  in- 
consistent or  unpatriotic,"  may  be  analyzed ;  "  If 
he  joined,  etc.,  he  was  inconsistent ;"  "  If  he  did 


Sec.  XL]  JUDGMENT.  105 

not  join,  etc.,  he  was  unpatriotic;"  "But  he  did  or 
did  not  join  f  "  He  was  either  inconsistent  or  un- 
patriotic." These  may  be  turned  into  Categoricals 
by  the  methods  already  prescribed. 


CHAPTER  IV. 

REASONING IMMEDIATE    INFERENCE. 

Section  I. — Introductory  Remarks. 

1.  The  next  stage  of  Thought  after  the  forma- 
Zoning  De-  tion  of  Judgments,  is  that  of  deriving 
fined.  from  judgments  given  other  judgments 
founded  upon  them.     This  is  Reasoning. 

2.  Reasoning  is  by  inference  from  one  Judgment 

to  another  derived  from  it :  or  from  two 

Media  ie  and  Im- 
mediate Infer-  judgments  to  a  third,  which  could  not 

be  derived  from  either  alone,  but  flows 
from  both  combined.  The  former  is  called  Reasoning 
by  Immediate  Inference,  the  latter  by  Mediate  In- 
ference, i.  e.  from  one  judgment  through  the  medium 
of  another ;  or  more  strictly,  as  it  will  more  fully 
appear,  through  a  middle  term,  mcdius  term  huts, 
common  to  both  the  judgments  given,  by  means  of 
a  common  or  opposite  relation  to  which,  the  two 

106 


Sec.  II.]  IMMEDIATE  INFERENCE.  107 

terms  of  the  conclusion  are  found  to  agree  or  disa- 
gree with  each  other.  These  two  kinds  of  reasoning 
will  be  severally  treated  in  their  order. 

3.  Immediate  Inference,  i.  e.  infer-  Three  kinds  of 

n  •    j  i     r»  xi  Immediate   In- 

ence  of  one  judgment  irom  another,  is  f 
of   three    kinds,    termed    Opposition,  opposition,  Con- 
Conversion,  and  Equipollence  or  Infi-  ^Jf011'    *f" 

7  *•     x  pollence  or  Inn- 

nitation.     And  first  of,  nitation. 

Sect.  II. — Opposition. 

4.  Opposition  exists  between  judgments  having 
the  same  subject  and  predicate,  but  dif-  opposition  de- 
fering  in  quantity,  or  quality,  or  both.  fined< 
Thus,  "  all  A  is  B,"  and  "some  A  is  not  B,"  are  op- 
posed. They  differ  both  in  quantity  and  quality. 
This  is  the  strongest  kind  of  opposition,  called  con- 
tradictory. From  any  judgment  whatever,  an  infer- 
ence can  be  made  regarding  its  contra- 

,  .  ,    .      ,  .,  .  Contradictories. 

dictory,  or  which  is  the  same  thing,  any 
affirmation  or  denial  regarding  either  of  two  con- 
tradictories, warrants  an  inference  in  regard  to  the 
other.  Thus,  if  we  take  the  two  contradictories, 
"  all  men  are  mortal/'  "  some  men  are  not  mortal/' 
when  either  is  true  the  other  is  false ;  when  either  is 
false  the  other  is  true. 


108 


LOGIC. 


[Chap.  IV. 


5.  Besides  the  Contradictories,  we  have  the  Con- 
traries A  and   E,  and   the   Sub-Con- 
Contraries, 

Sub-Contraries,  traries  I  and  O,  which  respectively  dif- 
fer in  quality  alone.  Also  the  Subal- 
terns A  and  I,  E  and  O,  in  which  the  members 
of  each  respective  pair  differ  from  each  other  only 
in  quantity.  In  each  pair  of  these  the  Universal  is 
Snbaiternans.  called  the  Subalternans,  the  Particular 
Snbaltemate.  the  Subalternate.  All  these  forms  of  op- 
position are  brought  compactly  and  clearly  to  view 
by  the  following  ingenious  and  simple  diagram, 
which  has  been  devised  by  logicians. 


Contraries. 


E 


to 

'a 

XJ1 


&/ 

{; 

CD 


Sub-contraries. 


0 


Sec.  II.]  IMMEDIATE  INFERENCE.  109 

6.  The  Laws  of  Inference  in  the  case  of  judg- 
ments in  Opposition  are,  in  brief,  as  fol-  Laws  of  Infer- 
ence in  Opposi- 
10WS :  tion. 

a.  Of  Contradictories  one  or  the  other  must  be 
true,  both  cannot  be  true.  And  by  the  Ee-Contradicto- 
law  of  Excluded  Middle  no  interme-  ries* 

diate  between  them  can  be  true.  Therefore,  from 
the  truth  of  either  of  two  contradictories,  it  follows 
that  its  opposite  is  false ;  and  from  the  falsity  of 
either,  the  truth  of  the  opposite  may  be  inferred. 

b.  From  the  truth  of  either  Subalternans,  the 
truth  of  its  Subalternate  follows.    From 

•  i  i       Subalterns. 

its  falsity  nothing  follows  with  regard 
to  the  Subalternate;  from  the  truth  of  either  Subal- 
ternate nothing  follows  in  regard  to  its  Subalter- 
nans.    From   the  falsity  of  the  Subalternate  the 
falsity  of  the  Subalternans  results. 

c.  From  the  truth  of  a  Contrary  the  falsity 
of  the  opposite  Contrary  follows.     But 

Contraries. 

from  the  falsity  of  one  Contrary,  nothing 
follows  in  regard  to  the  other. 

d.  From  the  truth  of  either  Sub-Contrary  nothing 
follows  in  regard  to  the  other  Sub-Con- 
trary.    But  from  the  negative  of  one  of 
them,  it  follows  that  the  other  must  be  true. 


Sub-Contraries. 


10 


110  LOGIC.  [Chap.  IV. 

7.  From  this  it  appears  that  the  Opposition  be- 

tween Contradictories  is  far  the  most  im- 

Contradictory 

Opposition  most  portant  and  fruitful  of  inferences.    The 

Important.  •  i    1  1  i         j?  •  ,1 

*  most  available   mode  ot   proving   the 

truth  of  many  propositions,  is  to  prove  their  Con- 
tradictories false. 

8.  The   foregoing   view  exhausts   opposition  as 

between   the   four    fundamental  judg- 

OppositionTrea-  ments  A  E  I  and  O  above  recognized 
tedbytheJudg-  jjy  t]ie  0i<j  l0cricians.     But  if  we  bring 

ments  U  and  T.    /  m     *  p  & 

in  the  additional  substitutive  judgments 
U  and  Y  already  considered,  they  lay  a  founda- 
tion for  other  forms  of  Opposition. 

a.  For  other  forms  of  Contrary  Opposition.   The 

characteristic  of  this  kind  of  opposition 

Other  forms  of  rr 

Contrary  Oppo-  is,  that  of  two  judgments  opposite  in 
quality  but  not  in  quantity,  both  judg- 
ments may  be  false,  but  cannot  be  true  together. 
Thus  A  and  E  may  both  be  false,  but  cannot  both 
be  true  together.  But  the  same  is  true  of  E  and  U. 
Thus,  it  is  false  alike  that  "  no  men  are  poets/'  and 
that  "  all  men  are  all  the  poets."  It  is  true  that 
"  all  men  are  all  rational  animals,"  false  that  "  no 
men  are  rational  animals." 

b.  Out  of  the  Opposition  of  these  Substitutive 


Sec.  II.]  IMMEDIATE  INFERENCE.  \\\ 

Judgments  to  each  other,  and  to  other  judgments 
arises  what  has  been  named  Inconsistent  inconsistent 
Opposition.  This  obtains  bet  ween  judg-  °PPosltlon' 
ments  opposed  in  quantity  but  not  in  quality,  which 
cannot  both  be  true,  though  both  may  be  false,  at  the 
same  time.  Thus  the  opposed  judgments  A  and  U 
cannot  both  be  true  of  the  same  subject  and  predi- 
cate, unless  A  be  considered,  as  it  was  by  old  logi- 
cians, to  include  U.  It  cannot  be  true  that  all  men 
are  all  the  animals  (U),  and  that  all  men  are  only 
some  animals  (A).  But  A  and  U  may  both  be 
false,  as  in  any  subject  and  predicate  in  which  ne- 
gatives or  particulars  only  are  true. 

c.  Subaltern  Opposition  exists  when  there  is  more 
distribution  in  either  term  of  one  judg-  New  gubaltern 
ment  (the  Subalternans)  than  in  the  Opposition. 
corresponding  term  of  the  other  (the  Subalternate). 
Accordingly,  this  kind  of  opposition  exists  between 
U  and  I,  also  between  Y  and  I,  for  from  positing 
either  U  or  Y,  I  may  be  inferred.  But  from  I 
neither  U  nor  Y  can  be  inferred. 

9.  Applying  these  principles,  and  extending  the 
diagram  of  Opposition  already  given  to  include  U 
and  Y,  we  have  the  following  result : 


112 


LOGIC. 


[Chap.  IV. 


IT Inconsistent A Contrary E Contrary 


p 
o 
o 

P 
to 
i— »• 

CD 

rt- 
O 

P 


••<s 


c&V 


s^ 


02 

p 
p 

P 


'O  \P 

V 


<V 


CP 


P 
C 

*» 


CP 


*A 


.u 


p 

o 

p 

CD 


CD 
P 


Y*. Subaltern I* ....  Sub-contrary.. .".0*...  Sub-contrary...  Y* 


10.  Opposite  Judgments  must  have  the  same 
subject  and  predicate,  not  only  in  sound  but  in 
sense.  "  Bread  is  heavy,"  and  "  bread  is  not  heavy," 
are  not  opposed,  if  in  the  former  case  "heavy"  be 
used  to  denote  imperfect  fermentation,  in  the  latter 
to  denote  specific  gravity  as  compared  with  lead. 


*  Some  writers,  among  whom  is  Thomson  in  his  Laws  of 
Thought,  class  the  opposition  between  A  and  0,  as  Contrary  in- 
stead of  Contradictory,  and  admit  only  E  and  I  to  be  Contradic- 
tories. He  says,  "  "We  cannot  tell  from  the  removal  of  0  whether 
we  ought  to  replace  it  by  A  or  U."  This,  however,  though  theo- 
retically true,  hardly  calls  for  a  deviation  from  the  established 
use  of  terms  in  practice.  Would  not  this  argument  abolish  the 
contradiction  between  E  and  I?  If  E  be  removed,  we  do  not, 
from  that  fact,  know  whether  it  may  not  be  replaced  by  A,  U,  or 
Y,  as  well  as  I.  We  only  know  that  as  much  as  I  is  true.  In 
like  manner  we  know  that  certainly  as  much  as  A,  and  possibly 
as  much  as  U,  is  true  if  0  be  removed.  This  gives  them  both  the 
power  of  contradictories.  How  much  more  is  true  in  any  case 
must  be  learned  from  other  sources.  Y  is  a  kind  of  false  sub- 
contrary  to  0.     If  it  be  true,  0  is  true. 


Sec.  III.]  IMMEDIATE  INFERENCE.  H% 

Sect.  III. — Conversion. 

11.  A  second  mode  of  immediate  inference  is  by 
Conversion.  Propositions  or  judgments  Conversion  De_ 
are  converted  when  the  predicate  and  finedi 

the  subject  change  places,  in  such  a  way  that  the 
converse  is  an  inference  from  the  convertend  or 
judgment  converted. 

12.  In  order  that  Conversion  may  be  illative,  or 
give  rise  to  a  legitimate  inference,  no  Law  of  Distri. 
term  must  be  distributed  in  the  con-  bution  of  Terms. 
verse  which  was  not  distributed  in  the  convertend : 
otherwise  more  would  be  spoken  of  in  the  conclu- 
sion than  in  the  premise.  This  was  the  rule  of  the 
older  logicians. 

13.  Hamilton  and  his  school,  however,  maintain, 
not  only  that  no  term  should  be  distri-     Hamilton's 
buted  in  the  converse  which  was  undis-     LaWi 
tributed  in  the  convertend,  but  that  all  terms  dis- 
tributed in  the  latter  should  be  distributed  in  the 
former. 

14.  Conversion,  in  order  to  be  logical,  according 
to  these  principles,  sometimes  requires 

a  change  in  the  Quality  or  Quantity  of  ^yT  Q llm? 
the  convertend.     Hence  result  the  fol-  sometimes   ne- 

lowing  modes  of  Conversion. 
10*  H 


114  LOGIC.  [Chap.  IV. 

A.  Simple    Conversion    is  when    there    is    no 

Simple  Conver-   change     in     either    Quality     OV    Quan- 

sion'  tity. 

B.  Conversion  by  Limitation,  sometimes  called 
By  Limitation  Per  accidens,  is  when  the  quantity  is 
or  per  accidens.    changed  from  universal  to  particular. 

C.  When  the  quality  is  changed,  it  is  said 
Negation    and  to    be    by   Negation    or    Contra-posi- 

Contra-position.   ±' 

15.  Accordingly, 

a.  A,  which  distributes  the  subject  but  not  the 
How  to  Convert  predicate,  must  be  converted  by  Limi- 
A-  tation  from  universal  to  particular,  and 

therefore,  according  to  the  old  Logic,  which  does 

B  old  Lo  ic  A  no^  recognize  ^ne  distribution  of  affir- 
becomes  I,  mative  predicates,  becomes  I ;  but  with 
a  quantified  and  distributed  predicate  it  becomes 
Y.  Thus,  "all  men  are  mortal,"  becomes  in  the 
former  method,  "some  mortals  are  men,"  which  is  I; 
and  in  the  latter  method,  "some  mortals  are  all  men," 

In  perfect  Con-   which   is   Y'      **   is  JUStl7  argUed  that 

version  A.  be-  the  latter  is  the  only  perfect  Conversion, 

comes  I. 

because  it  alone  enables  us,  by  recon- 
version to  regain  the  original  convertend.  This 
ought  to  be  possible  in  thorough  conversion.     From 


Sec.  III.]  IMMEDIATE  INFERENCE.  \\§ 

"  some  mortals  are  men,"  i.  e.  "  some  men,"  we  can 
only  get  by  re-conversion,  "  some  men  are  mortals." 
But  from  "  some  mortals  are  all  men,"  we  readily 
get  back  the  original  convertend,  "all  men  are 
mortals."     Of  course  from  U  comes  I, 

.,,,,.  U  involves  I. 

its  subalternate. 

b.  E.,  which   distributes    both    terms,   may   be 
converted  simply,  and  remains  E  after      E  converted 
conversion.     If,  "  no  men  are  angels,"     slm&Y' 
then  "  no  angels  are  men." 

c.  In  like  manner  I,  which  distributes  neither 
term,  may  be  converted  simply.       If 

some  Americans  are  Indians,  then  some 
Indians  are  Americans. 

d.  O  distributes  the  predicate  but  not  the  subject. 
Consequently,  if  it  were  converted  with-  '  _  , 

x  J  7  0  converted  oy 

out  changing  its  quality,  the  subject  un-  contraposition 
distributed  in  the  convertend,  would  be 
distributed  in  the  converse  by  being  the  predicate 
of  a  negative.  Thus,  "  some  quadrupeds  are  not 
horses,"  would  become  "  some  horses  are  not  quad- 
rupeds," which  is  obviously  illogical  as  well  as 
false. 

In  order  to  avoid  this,  the  negative  particle  is 
transferred  from  the  copula  to  the  predicate,  so  that 


116  LOGIC.  [Chap.  IV. 

the  convertend  becomes  I,  which  may  be  simply  con- 
verted.     Thus,   for   "some    quadrupeds    are   not 

Pred. 

I ! 

horses/'  say, " some  quadrupeds  are  jnot  horses!,"  or 
"  things  not  horses."  This  is  I,  which  converted 
simply  becomes,  "  some  things  not  horses  are  quad- 
rupeds."    Here  conversion  is  by  contraposition. 

16.  A  and  U,  i.  e.  all  affirmatives  which  have 
Conversion  of  A  the  subject   distributed  admit  of  this 

and  U  by  con-  ,  -mi 

traposition.        sort  of  conversion,     lhus, 


A.  "  All  men  are  rational,"  may  be  converted  into 

E.  "  Whatever  is  not  rational  is  not  a  man." 

U.  "  All  men  are  rational  animals,"  may  become 

E.  "  Whatever  is  not  a  rational  animal  is  not  a  man." 

17.  U  may  be  converted  simply.     Thus,  "All 

men  are  rational  animals."     Therefore, 

U  converted 

simply   and      "  All  rational  animals  are  men."  This  is 

thence  into  I.        jj  ^  by  subalternation  will  gi  ve  J  a]so, 

Y  may  be  converted  into  A,  which  by  subalter- 
nation yields  I.      Thus,   "Some  men 
are  poets"  (i.  e.  all  the  poets),  yields  A. 
All  poets  are  men. 

18.  The  several  kinds  of  judgments  therefore 
Summation,     may  be  converted  as  follows : 


Sec.  IV.]  IMMEDIATE  INFERENCE.  \YJ 

A  may  be  converted  into  Y  and  thence  I. 
E  into  E,  and  thence  O. 
I  into  I. 

O  into  I  indirectly  by  contraposition. 
U  into  U,  and  thence  I. 
Y  into  A,  and  thence  I. 

A  and  U  may  also  be  converted  by  contrapo- 
sition. 

Sect.  IV. — Other  Modes  of  Immediate  Inference. 

19.  Besides    Opposition    and    Conversion,    the 
standard   modes  of  Immediate   Infer-  n , 

Other  forms   of 

ence  formerly  recognized  by  logicians,  Immediate  ln- 

i,i  r»  n  ',     i  ferencei 

several  other  torms  oi  it  deserve  men- 
tion. 

A.  By  Reciprocal  Change  of  Positive  and 
Privative  Conceptions. 

20.  If  we  take  any  pair  of  Positive  and  Priva- 
tive, or  as  they  are   styled   by  some, 

T    a    '*.  ±    l    n  ±*  i         up         Change  of  Posi- 

lnnnitated  Conceptions,  as  has  before  tive  and  priva. 
been  shown,  they  comprise,  taken  abso-  t|ve  Concep- 
lutely,  all  being,  or  the  universe :  and 
taken  most  narrowly,  they  include  all  the  members 
of  the  genus  which  is  the  particular  object  of 
thought.     Thus  "  virtuous  "  and  "  not  virtuous," 


118  LOGIC.  [Chap.  IV. 

taken  absolutely,  include  the  universe  of  actual  and 
possible  being.  But  practically,  they  are  only  used 
in  reference  to  beings  capable  of  virtue,  i.  e.  moral 
beings,  and,  in  ordinary  cases,  are  applied  to  none 
but  mankind.  Supposing  the  latter  to  be  spoken 
of,  all  are  included  in  the  virtuous  and  non-virtuous, 
and  whatever  men  are  not  one  are  the  other. 
T  ffi  th  Therefore,  to  affirm  a  Positive  Concep- 
Positive  is  to  tion  of  any  subject,  is  the  same  as  to 

deny  the  Priva-  .  , 

tive  and  vice  deny  its  corresponding  rrivative,  and 
versa,  v^ce  versctf     It  is  often  convenient  in 

such  cases,  instead  of  an  awkward  and  confusing  use 
of  the  particle  "  not,"  in  order  to  mark  the  Priva- 
tive contradictory,  to  use  the  particles  in  or  un  to 
form  a  single  compound  privative  word — as  incon- 
sistent for  not  consistent,  zmwise  for  not  wise — or  to 
use  any  word  of  corresponding  privative  import, 
without  any  explicit  negative  particle,  as  foolish  for 
unwise,  soft  for  not  hard. 

Knies  for  snch  ^1.  This  sort  of  immediate  inference 
Conversion.  \s  governed  by  the  two  following  rules. 
a.  If  the  predicate  be  changed  from  Positive  to 
Privative,  or  the  reverse,  change  the  quality  of  the 
judgment.     Thus,  "all  men  are  rational,  "no  men 


Sec.  IV.]  IMMEDIATE  INFERENCE.  H9 

are  (not  rational),  L  e.  irrational/'  and  by  conver- 
sion, "  no  irrational  beings  are  men." 

b.  To  change  the  subject  in  like  manner,  first 
convert  the  proposition :  thence  change  the  subject 
(now  become  predicate),  from  positive  to  privative 
or  the  reverse,  and  change  the  quality  of  the  judg- 
ment. Or,  (what  is  the  same),  convert  the  judgment, 
and  proceed  as  in  rule  first.     Thus, 

"  Some  men  are  (all  the)  poets."     By  conversion, 

"Some  (or  all)  poets  are  men." 

"  Some  (or  all)  poets  are  not  beings  who  are  not  men." 

"  No  trees  are  stones."     By  conversion, 

"  No  stones  are  trees." 

"  All  stones  are  things  not  trees." 

These  methods  of  immediate  inference  may  be 
applied  to  all  the  varieties  of  propositions. 

B.  Immediate  Inference  from  Disjunctives 
or  Partitives. 

22.  In  a  Disjunctive  or  Partitive  Judgment,  it  is 
immediately  evident  that  whatever  of 

From    Disjunc- 

the  objects   included   in  it  belongs  to  tives  and  Par- 

n  -.  i  •  ,    •      i    j   j    •      titiveSi 

one  of  its  members,  is  not  included  in 

any  of  the  others,  and  whatever  is  not  included  in 

it,  does  belong  to  one  of  the  others.     Thus,  "  The 


120  LOGIC.  [Chap.  IV. 

seasons   are   either  Spring,   Summer,  Autumn,   or 
Winter."     "Spring  is  neither  Summer,  Autumn, 
nor  Winter,"  and  "  whatever  seasons  are  not  Spring, 
are  either  Summer,  Autumn,  or  Winter." 
C.  From  a  Combination  of  Predicates. 

23.  If  it  be  known  of  man  that  he  is  rational, 

Bv  uniting  Pre-   a^S0    ^na*    ne   *S    an^ma^    a^so    that    he 

dicates.  laughs,  then  these  Predicates  may  be 

united  in  one  judgment,  which  may  be  A  or  U,  ac- 
cording to  circumstances — in  the  present  case  U — 
Thus :  "  Man  is  a  rational  animal  that  laughs." 
Other  Formulae  furnish  materials  for  immediate 
inference  too  numerous  and  obvious  to 

Other  Formula  .  .  p       .  , ,  TT  n 

require  minute  specification.  Howard 
was  a  philanthropist,"  therefore  philanthropy  has 
a  real  existence.  "  The  President  is  the  supreme 
executive,"  therefore  to  assail  the  President  is  to 
assail  the  supreme  executive. 

24.  Some  have  maintained  that  these  processes  of 

Immediate  Inference  are  unimportant, 

The  importance   ,  , ,  ,      .  .  .  -,  . 

of    Immediate  because  the  conclusion  contains  nothing 
Inference  no^  previously  contained  in  the  premise. 

shown, 

But  if  this  objection  be  valid  it  lies 
against  all  reasoning.  It  is  further  objected  that 
the  conclusion  is  identical  with  the  premise.     This 


Sec.  IV.]  IMMEDIATE  INFERENCE.  121 

is  an  error.     It  will  hardly  be  claimed  in  regard  to 
inference  by  opposition,  especially  con-        ,   . 

J      rr  .  J  Conclusion    not 

tradictory   opposition.      In   conversion  Identical  with 

n  i  •      ,  l         j  •  r\       the  Premise. 

the  subject  or  principal  notion  on  the 
judgment  is  changed.  Equivalent  changes  from 
the  premise  to  the  conclusion  occur  in  other  forms 
of  immediate  inference.  Few  persons  who  have  not 
made  Logic  a  study,  can  state  with  accuracy  the 
exact  illative  converse  of  any,  especially  of  all  the 
fundamental  logical  judgments,  as  they  understand, 
who  have  had  experience  in  teaching  Logic.  An 
eminent  logician  says,  "  Could  any  person  not  accus- 
tomed to  exercises  of  this  kind,  draw  out  fully  all 
his  own  meaning,  when  he  utters  the  simplest  pro- 
position? The  judgment  'all  men  Explication  of 
are  mortal*  (a  plainer  cannot  be  found),  "An  men  are 

mortal,"       into 

tells  us  that  man  is  one  species  in  the  other       jndg- 

class  of  mortal  beings — that  the  mark  ments' 

of  mortality  should  always  accompany  our  notion  of 

man — that  the  word  mortal  is  a  name  which  may 

rightly  be  given  to  man — that,  if  all  are  mortal, 

any  one  man  is — that  any  statement  which  affirms 

that  no  men  are  mortal,  must  be  quite  false — that 

even  the  statement  that  some  men  are  not  mortal  is 

equally  false — that  since  man  is  contained  in  the 
li 


^22  LOGIC.  [Chap.  IV. 

class  of  mortal  beings,  which  is  a  wider  class,  it 
would  be  wrong  to  say  all  mortal  things  are  men — 
that,  however,  the  assertion  "  some  mortals  are  men," 
would  be  true  enough — even  "  some  mortals  are  all 
men  " — that  no  men  can  be  immortal — that  any  im- 
mortal beings  must  be  other  than  men — that  mor- 
tality really  exists,  being  found  in  man,  whom  we 
know  to  exist — that  a  man  with  immortal  hopes  is 
a  mortal  with  immortal  hopes — that  (since  heaven 
is  immortality)  a  man  expecting  heaven  is  a  mortal 
looking  for  immortality — that  he  who  honors  a 
man,  honors  a  mortal.  Thus  from  this  simple 
judgment  fourteen  judgments  have  unfolded  them- 
selves, or,  as  some  would  say,  the  judgment  has  been 
put  in  fifteen  different  ways,  in  the  last  three  of 
which  only  is  any  new  matter  introduced.  And 
yet  any  man  of  common  sense  would  say  that  his 
proposition  really  implied  them." — Thomson's  Laws 
of  Thought,  pp.  191-2. 


CHAPTER  V. 

REASONING MEDIATE  INFERENCE. 

Section  I. — Introductory  Kemarks. 

Immediate  Inference,  as  we  have  seen,  is  of 
one  Judgment  from  another  without  the  interven- 
tion of  any  third  judgment  or  third  term. 

1.  Mediate  Inference  is  from  two  judgments 
given  as  premises  to  a  third  founded  Mediate  Infer- 
upon  them,  in  which  the  two  terms  of  f? is  from  tw° 

Judgments  giv- 

the  conclusion  are  found  to  agree  or  en  to  a  third. 
disagree  with  each  other,  through  a  third  or  middle 
term  with  which  they  have  each  been  Through  a  Mid- 
compared  in  the  premises.  Thus,  all  ^  Tern1, 
M  is  P,  all  S  is  M,  .-.  All  S  is  P.  Here  all  S  is 
declared  to  be  P,  because  it  has  previously  been 
affirmed  to  be  M,  and  all  M  to  be  P.  Or  if  we 
take  a  negative  conclusion,  "No  stones  are  trees, 
This  oak  is  not  a  tree,  .*.  It  is  not  a  stone."  Here 
oak,  in  the  conclusion,  is  declared  not  to  be  a  stone, 
because  it  is  a  tree,  and  no  trees  are  stones. 

123 


124  LOGIC.  [Chap.  V. 

2.  It  is  obvious   that  the  ultimate  ground  of 
Mediate  Inference,  as  shown  in  the  above  examples 
(and  the  same  may  be  shown  of  all  others),  is  re- 
ducible to  the  principles  of  Identity  and 

Founded     on 

identity  and     Contradiction  or  rather  Non-contradic- 

Contradiction.       . .  x     , -i      ~     ,  a        j  -p> 

tion.  In  the  nrst  case  fe  and  r  agree — are 

one  with  each  other, — because  they  each  agree  with, 

are  the  same  as,  M.     Oak  and  stone  do 

Illnstration,  ,  ..,  ,        .-.         ■,  .-, 

not  agree  with  each  other,  because  the 
one  is,  the  other  is  not,  a  tree.  To  say  that  they 
are  one,  would  therefore  be  a  contradiction. 

3.  This  process  of  reasoning  from  two  judgments 
given,  to  a  third  derived  from   them,  through  a 

middle  term,  is  called  an  Argument, 

(from  Argumentum,  proof)  and,  when 

stated  in  regular  logical  form,  so  that  the  connection 

of  the  premises  with  the  conclusion  is  immediately 

evident :  it  is  called  a  Syllogism,  aollo- 

yiafxoq^    i.  e.  collecting    the    elements 

given  in  the  premises  into  a  conclusion. 

4.  The  subject  of  investigation  now  before  us, 
therefore,  is  the  doctrine  of  Syllogisms. 

A  Syllogism,  like  all  other  reasonings,  consists  of 

Parts  of  the    two  Parts,  that  which  is  to  be  proved, 
Syllogism.         ancj  t]iat  j3y  wnicn  it  is  to  be  proved. 


Sec.  I.]  MEDIATE  INFERENCE.  125 

Of  these,  in  whatever  order  they  may  stand,  the 
latter  are  called  the  Premises.     These 

.  __  .  .  ,r,  Premises. 

Premises  are  Major  and  Minor. 

The  Major  Premise  is  that  in  which  the  Major 
Term   is   compared  with   the  Middle, 

,     ,  i        ,i  i  i  •  i      Major  Premise. 

whatever  may  be  the  order  in  which 
they  stand. 

The  Minor  Premise  is  that  in  which 
the  Minor  Term  is  compared  with  the 
Middle. 

The  Premises,  as  the  word  implies,  are  put 
before  the  Conclusion,  when  the  syllo-      * 

J  Order  of  Premi- 

gism   is    arranged   in    regular   logical  ses  and  Oouciu- 

order.     Thus : 

"  All  conquerors  are  tyrants. 
Buonaparte  was  a  conqueror. 
He  was  a  tyrant." 

In  this  case  the  Conclusion  is  connected  with  the 
Premises  by  some  inferential  particle,  such  as 
"  therefore/'  "  hence,"  etc. 

But  it  is  more  common,  and  quite  as  natural,  to 
adopt  the  reverse  order  in  actual  reasoning — to  put 
the  Conclusion  first  and  the  Premises  afterward. 
Thus  :  "  Buonaparte  was  a  tyrant  for  he  was  a  con- 
queror, and  all  conquerors  are  tyrants."  And  fre- 
11* 


^26  LOGIC.  [Chap.  V. 

quently,  in  either  case,  not  more  than  one  premise  is 
expressed,  the  other  being  understood  and  obvious. 
Thus :  "  Many  voters  are  tools  of  demagogues  be- 
cause they  are  ignorant."  "  Free  government  will 
continue  since  the  people  are  virtuous."  This,  re- 
gularly drawn  out  would  be, 

"  A  virtuous  people  will  preserve  a  free  government. 

This  people  is  virtuous. 
.*.  It  will  preserve  a  free  government." 

A  Syllogism  in  which  the  premises  are  stated 
first  is  called  Synthetic,  because  it  puts 

Synthetic     and  .  .  ,  r 

Analytic  Sylio-  together  the  premises  in  order  to  form 

gisms,  ^e  conclusion# 

When  the  conclusion  is  stated  first,  it  is  called 
Analytic,  because  this  conclusion  is  analyzed  into  the 
proofs  out  of  which  it  grows. 

The  Major  Term  is  the  predicate  of 

Major  Term,      ,,      ^        , 

the  Conclusion. 

The  Minor  Term  is  the  subject  of  the 

Minor  Term,      ~        , 

Conclusion. 
Hence  every  Syllogism  must  have  three,  and  but 
HasthreeJndg-  three,  Judgments.     The  Major  Premise, 
ments.  the  Minor  Premise,  and  the  Conclusion 

in  which  the  major  and  minor  terms  are  compared 
with  each  other. 


Sec.  I.]  MEDIATE  INFERENCE.  127 

Every  Syllogism  must  have  three,  and  but  three, 
Terms;  the  Major,  Minor,  and  Middle. 
If  there  be  four  Terms,  either  in  form 
or  in  fact  (from  the  ambiguity  of  either  of  them), 
the  two  terms  of  the  conclusion  will  not  have  been 
compared  with  one  Middle  Term,  and  no  conclu- 
sion can  follow. 

5.  From  the  principles  of  Identity  and  Contradic- 
tion, the  following  Canons  for  testing  Canong  of  the 
the  validity  of  all  Syllogisms  result.        Syllogism, 

a.  If  the  Major  and  Minor  Terms,  each  being 
compared  with  the  same  third  or  Mid-  „ 

r  Canon  of  Affir- 

dle  term,  both  agree  with  it,  they  agree  mative  Conclu- 
with   each  other.     This   underlies   all 
Affirmative  Conclusions. 

b.  If  of  the  Major  and  Minor  Terms,  both  being 
compared  with  the  same  third  term,  one  of  Negative 
agrees  and  the  other  disagrees  with  it,  Conclusions. 
they  disagree  with  each  other.  This  is  the  founda- 
tion of  Negative  Conclusions.  Therefore  if  one 
premise  be  negative,  the  conclusion  must  be  negative. 

c.  If  they  both  disagree  with  the  same  third 
term,  no  conclusion  follows  as  to  whether  ,T      . 

7  .  Negative    Pre- 

they  agree  or  disagree  with  each  other,  mises  give  no 
This  is  the  case  of  Negative  Premises, 


128  LOGIC.  [Chap.  V. 

from  which  there  can  be  no  Conclusion.  Thus, 
from  "A  bird  is  not  a  sheep,"  "a  robin  is  not  a 
sheep" — nothing  can  be  inferred. 

d.  The  Middle  Term  must  be  distributed  at  least 

once   in   the    premises,    otherwise    the 

Middle      Term         _  . 

must  be  Distri-  Minor  Term  may  be  compared  with  one 
part  and  the  Major  with  another  part 
of  it.     From, 

"Some  men  are  poets, 
Some  men  are  Indians," 

Nothing  follows. 

Plurative  Judgments,  however,  give  rise  to  a 
peculiar  class  of  valid  Syllogisms  with  an  undis- 
tributed middle.     Thus : 

"  Most  men  have  some  kind  of  religion, 

Most  men  are  uncivilized, 
.'.  Some  uncivilized  persons  have  some  kind  of  religion." 

The  same  is  true  of  numerically  definite  Judg- 
ments.    Thus : 

"60  out  of  every  100  are  unreflecting, 

60  out  of  every  100  are  restless, 
.*.  20  out  of  every  100  restless  persons  are  unreflecting." 

e.  No  term  may  be  distributed  in  the  conclusion 


Sec.  I.]  MEDIATE  INFERENCE.  129 

which  was  not  distributed  in  the  premises.     This, 
which   is   Illicit  Process,  is   furtively  No  Illicit  pro. 
speaking   of   more   in   the   conclusion  cess" 
than  was  contained  in  the  premises.     Thus : 

"All  beasts  are  animals, 
Birds  are  not  beasts, 
They  are  not  animals." 

/.  From  Particular  Premises,  of  which  Y  is  not 
one,*  nothing  can  be  inferred.     With 

Particular  pre- 

none  but  the  particular  judgments  I  mises  give  us  no 

3  /-v      a  ,  1         ill      •   •  •      x l  Conclusion. 

and  O  oi  the  old  logicians  in  the  pre- 
mises, no  conclusion  can  follow,  because,  if  both 
were  I,  no  term  would  be  distributed,  whence  would 
result  an  undistributed  middle.  From  "some  men 
are  heroes,"  and  "some  men  are  poets/'  nothing 
can  be  inferred.  If  both  premises  be  O,  they  are 
both  negative,  and  no  conclusion  can  follow.  If 
one  be  O  and  the  other  I,  the  middle  term  must  be 
the  predicate  of  O  in  order  to  be  distributed,  and  in 
that  case  all  the  other  terms  will  remain  undistri- 

*  The  following  is  a  valid  conclusion  from  the  particular  judg- 
ments Y  and  I. 

Y.  Some  trees  are  all  the  oaks. 
I.    Some  oaks  are  white  oaks. 
..*.    Some  white  oaks  are  trees. 
I 


130  LOGIC.  [Chap.  V. 

buted.  But,  one  premise  being  negative,  the  con- 
clusion must  be  so  likewise.  This  would  distribute 
the  major  term  in  the  conclusion,  which  by  suppo- 
sition was  undistributed  in  the  premises.  Illicit  pro- 
cess results.     Thus: 

"Some  men  are  not  cultivated, 
Some  poets  are  cultivated, 
Some  poets  are  not  men." 

g.  If  either  Premise  be  particular,  the  Conclu- 
Conclusion  par-  si°n  must  be  Particular.  In  other 
ticuiar     when  Words,  a  universal  conclusion  requires 

either    premise 

is  so.  both  premises  to  be  universal. 

If  the  universal  conclusion  be  A,  then  the  sub- 
ject of  it  must  be  distributed  in  the  premises,  and 
must  therefore  be  the  subject  of  one  of  them,  since 
being  both  affirmative,  neither  can  distribute  the 
predicate.  For  the  same  reason  the  middle  term 
will  be  undistributed  in  that  premise,  being  then 
the  predicate  of  an  affirmative.  Therefore  the 
middle  term  must  be  the  subject  of  the  other  pre- 
mise, which  must  also  be  universal,  in  order  that  it 
may  be  distributed.  Thus  a  universal  affirmative 
conclusion  requires  both  premises  to  be  distributed. 

If  the  universal  conclusion  be  E,  then  both  its 
terms  must  be  distributed  in  addition  to  the  middle 


Sec.  I.]  MEDIATE  INFERENCE.  131 

term  the  premises.  This  requires  both  premises  to 
be  universal  and  one  of  them  negative,  or  both  nega- 
tive and  one  universal.  The  latter  is  impossible  as 
no  conclusion  can  come  from  two  negative  premises. 
Therefore  the  premises  must  be  both  universal. 

The  principle  that  one  negative  or  one  particular 
premise  renders  the  conclusion  respectively  nega- 
tive or  particular,  logicians  have  expressed  by 
saying  that  the  conclusion  follows  the  weaker  part. 
The  whole  of  these  canons  have  been  condensed 
into  the  following  Latin  lines : 

"  Distribuas  medium  nee  quartus  terminus  adsit, 
Utraque  nee  prsemissa  negans,  nee  particularis : 
Sectetur  partem  conclusio  deteriorem, 
Et  non  distribuat  nisi  cum  prsemissa,  negetve." 

This  reasoning,  however,  applies  only  to  syllo- 
gisms in  the  old  Logical  Judgments,  A  E  I  and  O. 
Syllogisms  with  U  or  Y  in  the  premises,  may  have 
universal  conclusions  with  one  premise  particular. 
Thus: 

U.  "  All  men  are  rational  animals, 
Y.     Some  men  are  all  the  poets, 

All  the  poets  are  rational  animals." 

A.  "  All  men  are  rational, 
Y.     Some  men  are  all  the  Polynesians, 
All  the  Polynesians  are  rational." 


132  LOGIC.  [Chap.  V. 

U.  "  Animals  are  all  bodies  having  sensation, 
Y.  Some  animals  are  all  oysters, 
.*.   All  oysters  have  sensation." 

Sect.  II. — Moods. 
{For  Moods  as  affected  by  Substitutive  Judgments,  see  Appendix  B.) 

6.  The  Mood  of  a  Syllogism  is  the  relation  of  its 
several  judgments  to  each  other,  with 

Mood  Defined.  „  .     . 

reference  to  their  respective  quantity 
and  quality,  these  being  designated  by  the  symbolic 
letters  A  E  I  O.  The  Mood  of  a  syllogism,  whose 
premises  and  conclusions  are  universal  affirmatives 
thus  becomes  AAA.  If  the  major  premise  were 
universal  affirmative,  the  minor  universal  negative, 
and  the  conclusion  universal  negative,  it  would  be 
A  E  E,  etc.,  etc. 

The  possible  combinations  of  these  four  kinds  of 
Number  of  propositions  are  of  course  4X4X4  = 
Moods.  6^     j>u£  most  of  these  are  invalid  as 

involving  violations  of  some  of  the  preceding  canons. 
Thus  E  E  E,  E  O  O,  and  others,  are  bad  on  account 
of  negative  premises.  I  O  O  and  others,  for  parti- 
cular premises.  I  E  O,  for  illicit  process.  Sifting 
Only  eleven  ou^  a^  mo°ds  that  are  thus  invalid,  only 
valid  Moods,  eleven  valid  ones  remain.  And  of  these 
only  a  part  are  valid  in  any  one  figure. 


Sec.  III.]  MEDIATE  INFERENCE.  133 

Sect.  III. — Figure. 

7.  The  Figure  of  a  Syllogism  depends  upon  the 
situation  of  the  Middle  Term  in  the  premises. 

The  Figures  as  fixed  by  Aristotle  were  three. 
The  first  and  normal  figure  is  when  the  Figures  of  Aris- 
middle  term  is  the  subject  of  the  major  totle' 
and  predicate  of  the  minor.  In  the  second,  the 
middle  term  is  the  predicate  of  both,  and  in  the  third 
the  subject  of  both.  The  fourth,  which  is  reputed 
to  have  been  introduced  by  Galen,  and  is  largely 
dropped  by  logicians  as  an  awkward  and  useless  in- 
version of  the  first,  occurs  when  the  middle  term  is 
made  the  predicate  of  the  major,  and  subject  of  the 
minor  premise.  Taking  S,  M,  and  P,  respectively, 
for  minor,  middle,  and  major  terms,  the  figures 
would  be  represented  thus : 

1st  Fig.  M  P.         2d.  P  M.        3d.  M  P.         4th  P  M. 
S   M.  S  M.  M  S.  M  S. 

S    P.  S  P.  S    P.  S  P. 

Sub.  Pr£e.;       Turn  Prae.  Prfe. ;     Turn  Sub.  Sub.;     Turn  Prse.  Sub. 

8.  Of  the  eleven  valid  Moods,  some  are  Invalid 

in  one  figure  which  are  valid  in  another.  yalid  and  - 

Thus  A  E  E  would   be  valid   in   the  valid  Moods- 

second  figure,  as, 
12 


134  LOGIC.  [Chap.  V. 

"  All  men  are  mortal, 
No  angels  are  mortal, 
V  No  angels  are  men." 

But  in  the  first  figure,  it  would  involve  illicit 
process  of  the  major  term.     Thus : 

"  All  birds  are  animals, 
No  reptiles  are  birds, 
.*.  No  reptiles  are  animals." 

The  only  valid  moods  in  the  first  figure  are  A  A 
A,  E  A  E,  A  1 1,  E  I  O.  As  this  is  the  mood  into 
which  the  normal  syllogism  falls,  logicians  have 
usually  unfolded  the  principles  which  govern  the 
syllogism  primarily  with  reference  to  that,  and  have 
devised  ways  of  converting  syllogisms  in  the  other 
figures  into  it,  and  subjecting  them  to  its  tests.  The 
canons  which  have  been  presented,  however,  apply 
immediately  to  the  syllogisms  in  all  the  figures. 

9.  As  is  their  wont,  logicians  have  wrought  out 
mnemonic  lines  in  Latin  to  designate  the  valid 
moods  and  syllogisms  in  the  several  figures,  with 
the  modes  of  reducing  the  subordinate  figures  to 
the  first. 

j-bArbArA,    cElArEnt,    dArll,    fErlOque    prio- 
ns. 


Figure  1.  \ 


„   rcEsArE,     cAmEstrEs,     fEstlnO,     bArOkO     (or 
Figure  2.< 

l     fAkOrO),  secundse. 


Sec.  III.].  MEDIATE  INFEREXCn.  lgg 

'tertia,  dArAptl,  dlsAmls,  dAtlnl,  fElAptOn, 
Figure  3.  -I  bOkArdO  (or,  dOkAmO),  f ErlsO,  habet,  quarta, 
insuper  addit, 

rbrAmAntip,  cAmEnEs,  dlmAarln,  fEsApo 
FigUrc4Jl      frEsIsOn. 

In  the  foregoing  lines  the  vowels  signify  the 
moods  of  the  syllogisms  respectively  al-  Erplanation  of 
lowablein  each  figure.  The  initial  letters  Mnemonic 
b,  c,  d,  f,  denote  that  the  syllogisms 
having  them  in  the  lower  figures  are  to  be  reduced 
to  the  corresponding  ones  in  the  first,  m  indicates  that 
in  doing  this,  the  premises  are  to  be  transposed,  s 
and  p  that  the  proposition  denoted  by  the  vowel 
immediately  preceding,  is  to  be  converted,  s,  simply 
p,  per  aeddensy  i.  e.  by  limitation  of  quantity  from 
universal  to  particular. 

10.  A  slight  examination  of  the  three  first  figures 
—and  for  practical  purposes  the  fourth  Limitationg 
may  at  present  be  passed  by — will  show  npon  the  several 
that,  in  the  First  Figure,  the  minor  pre- 
mise must  be  affirmative  in   order  to    Upon  the  1st. 
escape  illicit  process  of  the  major  term 
or  negative  premises,   and   that   consequently  the 
major  premise  must  be  universal  in  order  to  distri- 
bute  the   middle   term.     The   Second    Upon  the  2d. 


136  LOGIC.  [Chap.  V. 

Figure  can  prove  only  negatives,  because  the  mid- 
dle term,  being  a  predicate  in  both  premises,  re-« 
quires  at  least  one  negative  premise 
to  distribute  it.  The  Third  Figure 
yields  only  particulars,  because  the  major  and  minor 
terms,  being  both  predicates,  can  only  be  distributed 
by  having  their  respective  premises  negative.  But 
only  one  of  these  can  be  negative,  and  if  either  be  so 
it  must  be  the  major,  for  if  it  be  the  minor,  it  will 
make  the  conclusion  negative,  and  thus  distribute 
the  major  term,  which,  in  this  case,  would  be  un- 
distributed in  the  premises — thus  bringing  in  illicit 
process  of  the  major. 

11.  It  must,  however,  be  remarked,  that  these 
Exceptions  to  properties  of  the  several  figures  will  be 
t  e  oregomg  in  ~rea£}y  modified  in  the  case  of  the  iudff- 

tne  case  of  pre-   °  J  J       ° 

mises  u  and  Y.  ments  in  U  and  Y,  which  afford  dis- 
tributed affirmative  predicates,  and  therefore  cure 
all  faults  of  the  syllogism  arising  from  the  non- 
distribution  of  affirmative  predicates.  Inasmuch 
as  it  does  not  appear  from  the  mere  form  of  ex- 
pression that  any  affirmatives  distribute  their 
predicates,  it  is  always  presumed  that  they  do  not, 
unless  proved  by  other  evidence.  The  analysis  of 
the  normal  syllogism  and  its  properties  is  therefore 


Sec.  III.]  MEDIATE  INFERENCE.  137 

conducted  on  this  presumption.  But  if  the  judg- 
ments usually  classed  as  A  and  I,  can  in  any  case  be 
shown  to  be  U  and  Y  in  the  syllogism,  then  neither 
of  the  foregoing  limitations  in  respect  to  the  several 
figures  will  hold.  Thus,  with  these  substitutive 
judgments,  as  premises,  the  first  figure  may  have  a 
negative  minor  without  either  illicit  process  or 
negative  premises.     Take  the  example, 

U.  "  All  men  are  (all)  rational  animals, 
(Negative  Minor.)  E.     No  angels  are  men, 

No  angels  are  rational  animals." 

Again, 
(Particular  Major.)         "  Some  poets  have  genius, 

Y.     Some  men  are  (all  the)  poets, 
Some  men  have  genius." 

Again  in  the  second  figure, 

U.  "  Rational  animals  are  men, 
A.     Poets  are  men, 
(Affir.  Conclusion.)  .*.       Poets  are  rational  animals." 

Also  in  the  third  figure, 

"  All  men  are  mortal, 
U.       All  men  are  (all)  rational  animals, 
(Universal  Con.)    A.  .*.  All  rational  animals  are  mortal." 

This  is  the  proper  formula  of  the  Inductive  Syl- 
logism, which  naturally  falls  into  the  Formula  of  In- 

ductive    Syllo- 

third  figure,  and  could  not,  aside  from  a  gism, 
12* 


138  LOGIC.  [Chap.  V. 

substitutive  judgment,   yield  a  universal   conclu- 
sion.    Thus : 

"XYZ,  are  ruminant, 
X  Y  Z,  are  (as  good  as)  all  horned  animals, 
.*.  All  horned  animals  are  ruminant." 


Sect.  IV. — Maxims  by  which  different  logicians  have 

APPLIED   THE    PRINCIPLES  OF   IDENTITY   AND   CONTRADIC- 
TION to  the  Syllogism. 

12.  Most  of  these  are  founded  on  the  prin- 
Genus  Predica-  ciple  that,  in  a  normal  judgment,  the 
ted  of  Species.  Genus  is  predicated  of  the  Species,  and 
therefore  that  the  extension  of  the  subject  is  included 
in  that  of  the  predicate. 

A.  First  among  these  maxims  is  the  celebrated 
Aristotle's  Die-  Dictum  of  Aristotle,  that  whatever  can 
tum'  be  predicated  affirmatively  or  negatively 

of  any  class  or  term  distributed,  can  be  predicated 
in  like  manner  of  all  and  singular  the  classes  or  in- 
dividuals contained  under  it.  This  is  self-evident. 
Whatever  can  be  affirmed  or  denied  of  all  men,  can 
be  affirmed  or  denied  of  whatever  is  contained  un- 
der the   class   man.     This   maxim   is 

Directly  appli- 
cable to  First  directly  applicable  to,  and  illustrated 

by  the  First  Figure.     Thus : 


Sec.  IV.]  MEDIATE  INFERENCE.  139 

"  All  men  are  mortal, 
Poets  are  men, 
.'.  Poets  are  mortal." 

Here  mortal,  being  affirmed  of  the  genus  man,  is 

also  affirmed  of  the  species  poets  included  under 

it, 

"  No  men  are  brutes, 

Poets  are  men, 
.*.  They  are  not  brutes." 

Here,  what  is  denied  of  the  higher  class,  is  also 
denied  of  the  lower  class  or  species  included  in  it. 

B.  An  equivalent  maxim  is  that  founded  on  the 
relation  of  Whole  and  Parts,  that  what     wllole  and 
may  be  affirmed  or  denied  of  a  whole     Parts' 

(in  extension),  may  be  affirmed  of  its  parts,  i.  e. 
what  is  predicated  of  a  genus  may  be  predicated  of 
the  species  and  individuals,  or  the  parts  com- 
posing it.     Pars  partis  est  pars  totius. 

C.  To  the  same  effect  is  the  maxim  contention 
contenti  est  contentum  continentis.  Men,  the  content 
of  biped,  is  also  the  content  of  animal,  which  con- 
tains biped. 

D.  Kant's  formula  is,  nota  notaz  est  nota  rei  ipsius. 
This  probably  has  reference  to  construing  and  testing 
Syllogisms  according:  to  the  Intension  of  T       .    „  • 

J       fe  &  Intensive  Syllo- 

the  terms.     To  this  some  of  the  fore-  gisms, 


140  LOGIC.  [Chap.  V. 

going  maxims  apply,  but  in  a  reverse  order,  since 
the  whole  of  intension  increases  as  the  whole  of  in- 
tension decreases.  Therefore,  in  the  Intensive  Syl- 
logism, the  term  of  least  extension,  i.  e.  the  minor, 
becomes  the  greater  whole,  and  so  in  effect  the  major. 
Thus  the  Syllogism  according  to  extension, 

"  All  conquerors  are  brave, 
Caesar  was  a  conqueror, 
.'.  He  was  brave," 

according  to  intension  would  be  construed  thus: 

"  Csesar  was  a  conqueror,  i.  e.  had  the  mark  or  attribute  of  one, 

Conquerors  are  brave,  i.  e.  have  the  mark  of  bravery, 
.'.  He  had  the  mark  of  bravery  (was  brave)." 

Construed  either  way,  the  connection  of  the  same 
Conclusion  the  conclusion  with  the  same  premises,  is 

same  construed  n  ,    •  j  o 

,       t,  ,     .      equally  certain  and  necessary,     bome- 

by      Extension       x         J  J 

and  intension,  times  the  Extension,  sometimes  the  In- 
tension, is  more  prominent  in  the  mind  of  the  thinker. 
13.  The  relation  of  the  several  terms  of  the  Syl- 
Iliustration  by  logism  to  each  other  has  often  been  ex- 
Diagrams,  hibited  to  the  eye  by  Circular  Diagrams. 
Thus  the  Syllogisms  of  the  several  figures  may  be 
exhibited. 


Sec.  IV.] 


MEDIA  TE  INFERENCE. 


141 


Barbara. 


Celarent. 


1st  Figure. 


Darii. 


Ferio. 


1st  Figure. 


Cesare. 


Camestres,  etc.,  etc. 


2d  Figure. 


142 


LOGIC. 


[Chap.  V. 


Darapti. 


Felapton,  etc.,  etc. 


3d  Figure. 


For  a  fuller  view  of  the  different  schemes  of 
Syllogistic  Notation,  see  Appendix  B. 


Sect.  V. — Unfigured  Syllogism. 
14.  Before   leaving    this    subject,    it    is    proper 
How  Figure  dis-  ^°  ca^  attention  briefly  to  a  mode  of 
appears.  analyzing  the  Syllogism  introduced  by 

Hamilton,  which  dispenses  with  Figure  altogether. 
After  the  explicit  quantification  of  both  terms  of  a 
judgment,  the  relation  between  them  may  be  ex- 
pressed by  the  sign  of  equality,  and  either  of  them 
may  become  indifferently  subject  or  predicate.  In 
this  way  Figure  disappears.     If  we  say 

"  Men  are  rational, 
Negroes  are  men, 
.'.  Negroes  are  rational." 


Sec.  VI.]  MEDIATE  INFERENCE.  143 

we  may  more  explicitly,  though  awkwardly,  state 
our  meaning  thus ; 

"All  men  are  =  some  rational. 
All  negroes  are  =  some  men. 
.*.  All  negroes  =  some  rational." 

And  it  is  obvious  that  the  terms  of  either  or  all  of 
these  judgments  may  be  transposed,  without  impair- 
ing the  sense  or  reasoning.     Thus : 

"Some  rational  =  all  men. 
Some  men  =  all  negroes. 
.*.  Some  rational  =  all  negroes." 

All  other  figures  may  be  similarly  reduced.  It 
is  thus  apparent  that  the  Unfigured  Syllogism  ex- 
presses nakedly  the  essential  principle  which  under- 
lies reasoning  in  all  the  Figures. 

Sect.  VI. — Hypothetical  Syllogisms* 
15.  These  are  syllogisms  in  which  the  reasoning 

*  The  use  of  the  terms  "hypothetical"  and  "conditional,"  as 
applied  to  judgments  and  syllogisms,  varies  with  different  logi- 
cians. Some  use  the  word  hypothetical  to  denote  the  genus,  of 
which  they  make  conditional  and  disjunctive  the  species. 
Others  make  conditional  the  genus,  which  includes  hypothetical 
and  disjunctive  as  species.  That  is,  different  writers  make  the 
words  hypothetical  and  conditional  change  places. 


144  LOGIC.  [Chap,  V. 

turns  upon  the  Hypothesis  in  a  hypothetical  judg- 
ment.    A  syllogism  may  contain  hypo- 
Turns  on  the     thetical  judgments  in  which   the  rea- 
soning does  not  turn  upon  the  hypothe- 
Syiiogism  is     s*s>  but  simply  retains  it  as  one  of  the 

Categorical.         terms  Qf  the  conclusion#      Thus : 

"  Every  man  is  either  a  hero  or  a  coward, 
A.  B.  is  a  man, 
.*.  A.  B.  is  either  a  hero  or  a  coward." 

"  The  books  of  Scripture  are  entitled  to  reverence,  if  its  authors 

are  not  impostors, 
The  prophecies  are  books  of  Scripture, 
Therefore  the  prophecies  are  entitled  to  reverence,  if  their 

authors  are  not  impostors." 

Such  syllogisms  are  categorical. 

16.  But  when  the  Reasoning  turns  on  the  Hypo- 
H  th  t"  l  *nesis?  the  Syllogism  is  Hypothetical,  and 
Syllogism  De-  becomes  either  Conditional,  Disjunctive, 
or  Dilemmatic,  according  as  the  Hypo- 
thetical Judgment  on  which  it  is  founded,  falls  into 
one  or  the  other  of  these  classes.  In  these  syllo- 
gisms the  hypothetical  judgment  forms  the  major 
premise :  one  of  its  members  affirmed  or  denied  the 
minor — and  the  consequent  affirmation  or  denial  of 
some  other  member  forms  the  conclusion.     Thus : 


Sec.  VII.]  MEDIATE  INFERENCE.  145 

"Major.     If  rains  are  plenty,  the  crops  are  plenty, 
Minor.     The  rains  are  plenty, 
The  crops  are  plenty." 

Sect.  VII. — Conditional  Syllogisms. 
Conditional  Judgments  are  founded  on  the  prin- 
ciple   of   sufficient    reason,    otherwise     _ 

x  Grounded  in 

called  Reason  and  Consequent.  Eeason  and 

17.  The  nature  of  the   Conditional  ie(i™n  ■ 

Judgment  thus  being,  that  on  the  ground  of  Rea- 
son and  Consequent,  if  the  antecedent  is  true  the 
consequent  is  true,  it  follows ; 

A.  That,  if  the  Antecedent  be  affirmed  in  the 

minor  premise,  the  Consequent  must  be 

r  ^  Laws  of  Condi- 

affirmed  in  the  conclusion.  tional    Syllo- 

B.  If  the  Consequent  be  denied,  the    glsm" 
Antecedent  must  be  denied,  since,  if  the  latter  were 
true,  the  former  would  be  so  likewise. 

C.  If  the  Antecedent  be  denied  or  the  Consequent 
affirmed,  no  conclusion  follows,  for  the  latter  may  be 
true  or  the  former  false  on  other  grounds. 

Of  these  the  following  are  examples : 

A.  If  AisBCisD,  AisB,  .*.  C.  is  D. 

B.  If  A  is  B  C  is  D,  C  is  not  D,  .'.  A  is  not  B. 

r  If  A  is  B  C  is  D,  A  is  not  B,  .*.  no  conclusion. 

C.  < 

(■  If  A  is  B  C  is  D,  C  is  D,  .'.  no  conclusion. 

18 


146  LOGIC.  [Chap.  V. 

The  fallacy  of  any  inference  in  the  cases  under 

Fallacies  illus-   C>  wiU  aPPear   m0re   Plainly  fr0m  COn" 

trated.  crete  examples.     Thus,  if  we  deny  the 

antecedent,  the  following  example  will  show  that 

nothing  follows. 

"  If  James  is  a  drunkard  he  is  unfit  for  office, 
He  is  not  a  drunkard," 
.*.  Nothing  can  be  inferred. 

So  likewise  from  affirming  the  consequent  nothing 

follows.     Thus : 

"  If  the  people  are  virtuous  they  will  establish  schools, 

They  will  establish  schools," 
.*.  No  inference  is  warranted. 

No  fallacy  is  more  common  than  that  of  drawing 
inferences  in  such  cases. 

Sect.  VIII. — Disjunctive  Syllogisms. 
18.  These  are  founded  on  the  principle  of  Ex- 
cluded Middle.  Of  two  Contradictories, 

Eest  on  law  of 

Excluded  Mid-  one  must  be  true  and  the  other  false. 
There  is  no  other  alternative,  no  mid- 
dle ground.  Genuine  disjunctives  are  mutually 
exclusive.  That  is,  each  member  excludes  the 
others.  Whichever  is  true,  the  others  are  false.  If 
either  be  false,  some  one  of  the  others  is  true.  Thus, 
"  it  is  either  Spring,  Summer,  Autumn,  or  Winter." 


Sec.  VIII.]  MEDIATE  INFERENCE.  147 

Either  of  these  excludes  the  others.  Whichever  is 
true,  the  others  are  false.  Whichever  is  false,  some 
one  of  the  others  is  true.  Hence  with  a  disjunctive 
major ; 

First.  If  either  member  of  it  be  af- 

Laws  of  the  Dis- 

firmed    in  the  minor,  the   other  mem-  junctive  Byl- 
bers  are  false.     Thus :  °slsm' 

"  Men  are  either  angels,  brutes,  or  rational  animals, 

They  are  rational  animals, 
.*.  They  are  neither  angels  nor  brutes." 

This  is  what  the  logicians  call  modus  ponendo 
tollens. 

Second.  If,  in  the  minor,  either  member  of  the 
major  be  denied,  then  some  one  of  the  other  mem- 
bers is  true.  Thus,  in  the  preceding  example,  if  in 
the  minor  we  say,  "  Men  are  not  angels/'  it  follows 
that  they  are  either  brutes  or  rational  animals. 
This  is  7nodus  tollendo  ponens. 

19.  It  is  proper  to  repeat  that  a  Disjunctive 
may  be  turned  into  a  Conditional  by  _, 

Disjunctives 

taking  the  contradictory  of  one  of  its  turned  into  Con- 
members  for  the  antecedent.     "It   is 
either  Spring  or  Summer,"  is  the  same  as  "  if  it  is 
not  Spring  it  is  Summer."     Increasing  the  members 
thus :   "  It  is  either  Spring,  Summer,  Autumn  or 


148  LOGIC.  [Chap.  V. 

Winter" — we  get  by  conversion,  "if  it  is  not  Spring, 
it  is  either  Summer,  Autumn,  or  Winter." 

Sect.  IX. — The  Dilemma. 

20.  The  Dilemma  is  a  syllogism  having  a  Dilem- 
Dii  mma  De-  ma^c  Judgment  for  its  Major  Premise, 
fined.  with  a  Minor  so  affirming  or  denying 

some  member  or  members  of  the  major,  as  to  lay  the 
foundation  for  an  inference.  As  this  judgment  is  a 
combination  of  the  conditional  and  disjunctive,  so 
the  Dilemma  partakes  of  the  characters  of  the  con- 
ditional and  disjunctive  syllogism.  The  major  pre- 
mise of  the  dilemma  mav  be  of  various  forms,  each 
capable  of  different  minor  premises,  and  so  furnishing 
a  ground  for  different  conclusions. 

A.  The  Major  Premise  may  consist  of  one  An- 
Different  forms  tecedent  with  a  Disjunctive  Consequent. 
of  the  Dilemma,  jf  ^  ;s  g?  eitner  C  is  D  or  E  is  F.   Affirm 

One  Antecedent  m 

and  a  Disjunct-  the  Antecedent,  A  is  B,  and  the  Dis- 
ive  Consequent.  junctive  Consequent,  either  C  is  D  or  E 

is  F,  follows.  Deny  the  Consequent  wholly,  and  the 
Antecedent  must  be  denied.  If  neither  C  is  D  nor 
E  is  F,  then  A  is  not  B.  If,  however,  the  Conse- 
quent be  denied  only  disjunctively  nothing  can  be 
inferred,  for  if  either  member  of  the  Consequent  be 


Sec.  IX.]  MEDIATE  INFERENCE.  149 

true,  the  Antecedent  may  or  may  not  be  so.  As  in 
pure  conditionals,  from  the  mere  denial  of  the  Ante- 
cedent or  affirmation  of  the  Consequent,  nothing  can 
be  inferred. 

B.  There  may  be  a  Plurality  of  Antecedents  in 
the  major,  all  having  one  Common  Con-  Plurality  of  An- 
sequent.    If  A  is  B,  X  is  Y,  and  if  C  is  J?cedentB nand  a 

*  7  7  Common  Conse- 

D,  X  is  Y.  qnent. 

In  this  case,  if  the  Antecedents  be  wholly  or  dis- 
junctively granted,  the  one  Common  Consequent 
must  follow.  For  if  either  of  the  Antecedents  be 
true,  the  Consequent  is  true.  If  the  Consequent  be 
denied,  all  the  Antecedents  must  be  denied.  But 
from  affirming  the  Consequent  or  denying  either  or 
all  the  Antecedents,  nothing  can  be  inferred. 

C.  There  may  be  a  Plurality  of  Antecedents  in 
the  Major,  each  with  its  own  Conse-  plurality  of  An- 
quent.     In  this  case,  if  the  Antecedents  tec*dent+s'  each 

^  7  with    its    own 

be  affirmed  wholly,  the  Consequents  Consequent. 
may  be  affirmed  wholly.  If  the  Antecedents  be 
affirmed  disjunctively,  the  Consequents  may  be 
affirmed  disjunctively.  From  the  denial  of  Conse- 
quents wholly  or  disjunctively,  the  Antecedents 
may,  in  like  manner,  be  denied  wholly  or  disjunc- 
tively.    But  from  any  denial  of  the  Antecedents  or 

13* 


150  LOGIC.  [Chap.  V. 

affirmation  of  the  Consequents,  nothing  can  be  in- 
ferred. 

"  If  men  are  virtuous  they  are  wise, 
And  if  they  are  vicious  they  are  unwise ; 
But  they  are  either  virtuous  or  vicious, 
.*.  They  are  either  wise  or  unwise." 

Or  denying  the  Consequent  disjunctively, 

"But  either  they  are  not  wise  or  they  are  not  unwise, 
.'.  Either  they  are  not  virtuous  or  not  vicious." 

That  affirming  the  Antecedents  or  denying  the 
Consequents  wholly,  would  lead  to  a  correspond- 
ing affirmation  the  Consequents  or  denial  of  Ante- 
cedents respectively,  appears  in  the  following  ex- 
ample : 

"  If  A.  B.  is  diligent  he  will  prosper, 
And  if  C.  J),  is  wise  he  will  be  diligent, 
But  A.  B.  is  diligent  and  C.  D.  is  wise, 
.'.  A.  B.  will  prosper  and  C.  D.  will  be  diligent." 

In  like  manner  the  denial  of  both  Consequents 
involves  the  denial  of  both  Antecedents. 

Some  Logicians,  as  Whateley,  exhibit  that  alone 
as  the  only  true  Dilemma  which  has  a 

Kestriction     of 

the  Dilemma  by  plurality  of  Antecedents  in  the  Major, 

some  Logiciansi  n        -i.  .         ,•        -ivr* 

and  a  disjunctive  Minor. 
21.  The  Dilemma  has  been  named  the  Syllogis- 


Sec.  IX.]  MEDIATE  INFERENCE.  151 

mus  Cornutus,  or  Horned  Syllogism,  because  it  con- 
fronts an  adversary  with  two  assump-  Horns  f  ^ 
tions  or  arguments,  on  which  it  tosses  Dilemma. 
him  as  on  horns  from  one  to  the  other,  each  being 
equally  fatal  to  him.  Hence  the  common  phrase, 
"  Take  which  horn  of  the  Dilemma  you  will,  it  is 
equally  fatal  to  you."     Thus : 

"  If  things  are  what  we  can  help,  we  ought  not  to  fret  about 
them,  and  if  they  are  what  we  cannot  help,  we  ought  not  to  fret 
about  them.  But  all  things  are  either  what  we  can  or  cannot 
help.  .'.  They  are  what  we  ought  not  to  fret  about." 

22.  The   names   Trilemma,   Tetralemma,  Poly- 
lemma  have  been  sometimes  given  to  Trilemma   Te- 
this  sort  of  Syllogism  according  to  the  fralemma,  etc. 
number  of  members  or  horns,  if  they  exceed  two. 
Thus : 

"  If  A  is  B,  X  is  Y,  and  if  C  is  D,  X  is  Y,  and  if  E  is  F,  X 
is  Y.     But  either  A  is  B  or  C  is  D  or  E  is  F,  .*.  X  is  Y,"  is  a 

Trilemma. 

23.  The    ultimate    principles  which   determine 
the  resolution  of  the  Dilemma  are  those  ultimate  prin- 
which  determine  the  conditionals  and  ciPles- 
disjunctives  out  of  which  it  is  formed. 


152  LOGIC.  [Chap.  V. 

Sect.  X. — Incomplete  Syllogisms. 

24.  In  ordinary  reasoning,  it  is  seldom  that  the 
process  is  fully  expressed  in  a  completed  Syllogism. 
One  of  the  premises  is  often  wholly,  and  the  other 

partially    unexpressed.      A    syllogism 

with   one   premise   unexpressed   is   an 

Enthymeme.     Thus : 

"  The  Americans  are  a  free  people, 
.'.  They  are  happy.'' 

Here  the  unexpressed  Major  premise, 

"  All  free  peoples  are  happy," 

is  obvious.     In  this : 

"  Bankers  are  wealthy, 
.*.  A.  B.  is  wealthy," 

The  Minor  premise, 

"  A.  B.  is  a  banker," 

is  unexpressed. 

25.  Enthymemes,  like  Complete  Syllogisms,  often 

express  the  conclusion  with  "  because," 

Li  varied  forms.  , ,  -,      .  . .  -,         -,     . 

or  other  equivalent  particles,  between 
it  and  the  premise.     Thus : 

"  A.  B.  and  C.  are  unfit  to  vote  because  they  cannot  read." 
The  learner  will  readily  complete  such  a  Syllo- 
gism in  regular  form.     Indeed  the  forms  of  En- 


Sec.  XL]  MEDIATE  INFERENCE.  153 

thymerues,  occurring  in  ordinary  speech,  are  in- 
numerable.    Thus : 

"  These  men  are  good  and  therefore  brave,"  etc.,  etc. 


Sect.  XI. — Complex  Syllogisms. 
26.  Several  Syllogisms   may  be   combined   and 
abridged,  so  that  the  conclusiveness  of  the  reasoning 
shall  be  just  as  evident  as  if  they  were  all  fully  ex- 
pressed.    Chief  of  this  kind  is  the 

SORITES, 

Or  chain-syllogism,  in  which  a  number  of  syllo- 
gisms in  the  First  Figure  are  so'com- 

u*      j   xi    x  xi  t  p  xi      y     i  Sorites  defined, 

Dined,  that  the  predicate  01  the  first  pre- 
mise becomes  the  subject  of  the  next,  and  so  on, 
until,  in  the  conclusion,  the  predicate  of  the  last 
premise  is  predicated  of  the  subject  of  the  first. 
Thus : 

"  The  Hindoos  are  Asiatics, 
The  Asiatics  are  men, 
Men  are  rational  animals, 
Rational  animals  have  body  and  spirit, 
.'.  The  Hindoos  have  body  and  spirit." 

The  conclusiveness  of  this  may  be  represented 
thus: 


154 


LOGIC. 


[Chap.  V. 


27.  The  following  principles  control  the  Sorites. 
Principles  and  A.  ^he  several  unexpressed  proposi- 
laws  of  Sorites,  tions  are  respectively  conclusions  of 
each  next  preceding  syllogism.  Each  of  them  be- 
comes in  turn  the  minor  premise  of  the  next  follow- 
ing, as  will  easily  appear  by  completing  the  several 
syllogisms. 

B.  All  the  intermediate  expressed  premises, 
therefore,  between  the  first  and  the  conclusion,  are 
major.     The  first  alone  is  minor. 

C.  Hence  no  premise  except  the  first  can  be  par- 
ticular, for  the  first  figure  must  always  have  a  uni- 
versal major  in  order  to  distribute  the  middle  term. 

D.  Hence,  again,  no  premise  can  be  negative  ex- 
cept the  last;  for  a  negative  premise  would  make  the 
conclusion  negative,  which  in  turn  would  become  the 
negative  minor  premise  of  the  next  syllogism.     This 


Sec.  XI.]  MEDIATE  INFERENCE.  155 

has  been  shown,  in  the  first  figure,  to  beget  illicit 
process  of  the  major,  and  is  not  allowable.* 

GOCLENIAN   SORITES. 

28.  This  is  a  form  of  the  Sorites,  so  named  be- 
cause it  was  first  invented  or  brought 

,        /~i      i      •  T.      .        i  Inverted  Sorites, 

to  view  by  (jroclenius.     It  simply  in- 
verts the  order  of  the  premises  as  found  in  the  com- 
mon Sorites.     Thus,  if  we  take  the  example  before 
given,  it  can  be  stated  as  follows : 

"  Rational  animals  are  composed  of  body  and  spirit, 
Men  are  rational  animals, 
Asiatics  are  men, 
The  Hindoos  are  Asiatics, 
.•.  The  Hindoos  are  composed  of  body  and  spirit." 

In  this  form  of  Sorites,  each  preceding  subject 
becomes  the  predicate  of  the  next,  until,  in  the  con- 
clusion, the  predicate  of  the  first  premise  is  predi- 
cated of  the  subject  of  the  last.  The  last  premise 
alone  may  be  particular,  and  none  but  the  first  can 
be  negative. 

•  These  conditions,  however,  are  subject  to  any  exceptions 
which  might  arise  from  substitutive  judgments  in  any  of  the 
premises.     So  also  of  the  Sorites  in  every  form. 


156  LOGIC.  [Chap.  V. 

HYPOTHETICAL  SORITES. 

H    othetical  ^9.  It  is  plain  that  a  Sorites  may  be 

Sorites.  conditional  as  well  as  categorical.  Thus : 

If  A  is  B,  C  is  D, 

If  C  is  D,  E  is  F, 

If  E  is  F,  X  is  Y,  but  A  is  B, 
.'.  X  is  Y.     (Modus  ponens),  or  X  is  not  Y. 
.-.  A  is  not  B.     (Modus  tollens). 

In  regressive  form  thus: 

If  E  is  F,  X  is  Y, 

If  C  is  D,  E  is  F, 

If  A  is  B,  C  is  D.    But  A  is  B,  .*.  X  is  Y. 

Or  X  is  not  Y.  .'.  A  is  not  B. 

Direct  Form,      If  A  B  is  virtuous,  he  is  brave, 
If  brave,  he  is  magnanimous, 
If  magnanimous,  he  will  do  noble  deeds, 
But  he  is  virtuous,  .".  he  will  do  noble  deeds. 

PROSYELOGISM,  EPISYEEOGISM  AND  EPICHEIREMA. 

30.  The  different  forms  of  complex  Syllogisms 
comprise  the  modes  in  which  separate  syllogisms 
are  combined  into  wholes  of  connected  reasoning. 
In  these  the  Sorites  is  rare.  The  Prosyllogism  and 
Episyllogism  are  of  constant  occurrence. 

The  Prosyllogism  is  one  whose  conclusion  fur- 
Prosyllogism.  wishes  a  premise  for  the  principal  argu- 
Episyliogism.      ment.     The   Episyllogism   makes   the 


Sec.  XL]  MEDIATE  INFERENCE.  157 

conclusion  of  the  main  argument  one  of  its  pre- 
mises. 
"Useful  studies  ought  to  be  pursued : 

Prosyllogisrn. 
Logic  is  a  useful  study  (since  it  helps  to  think  well), 

Episyllogism. 
.'.  It  ought  to  be  studied,  and  (hence  an  educational  course 

which  omits  Logic  is  deficient)." 

31.  Epicheirema  denotes  a  Syllogism  which  has 

a  Prosyllogisrn  to  establish  each  of  its 

Epicheirema. 
premises.     Thus : 

"Man  has  a  spirit,  for  he  is  rational, 
And  he  has  a  body,  for  he  fills  space, 
.*.  Some  thing  that  has  a  spirit  has  body." 

This  name  is  also  applied  sometimes  in  cases 
where  there  is  a  single  Prosyllogisrn. 

Polysyllogism  is  a  combination  of  several  syllo- 
gisms in  one  argument.     The  Sorites  is 

Polysyllogism, 

one  species  01  it. 

14 


CHAPTER  VI. 

APPLIED   LOGIC — FALLACIES. 

1.  Having   brought   to  view  the   fundamental 

Transition  to  ^aws  °^  Pure  thinking,  or  principles  of 
Applied  Logic.  Formal  Logic,  as  related  to  Concep- 
tions, Judgments,  and  Reasonings,  it  remains  that 
we  now  treat,  as  briefly  as  possible,  of  the  applica- 
tion  of  these   principles,  first   to   the 

Fallacies.  ,  .  ,  .  ,  _ 

detection   and   avoidance  of   errors   m 

thinking;  and  next,  to  the  right  conduct  of  the 

thinking  process,  when  employed  in  the 

Method.  ,.  _  .    . 

discovery  ot  truth  as  pertaining  to 
actual  being.  The  former  brings  us  to  the  doctrine 
of  Fallacies,  the  latter  of  Method.*     And  first, 

Section  I. — Fallacies. 

2.  A  Fallacy  is  any  unsound  or  delusive  mode 
Fallacies  de-  °f  reasoning,  which  wears  a  specious 
fined.  appearance  of  being  genuine,  and  thus 

often  has  power  to  impose  upon  men. 

*  For  a  fuller  exhibition  of  the  difference  between  Formal  and 

Applied  Logic,  the  student  is  referred  to  the  observations  on  this 

subject  in  Chap.  L,  Sect.  IV. 
158 


Sec.  I.]  FALLACIES. 


159 


3.  Fallacies  are  divisible  into  Paralogisms  and 
Sophisms.  A  Paralogism  is  a  fault  in  Divided  into  Pa- 
reasoning  unknown  to  him  who  em-  ralosisms    and 

Sophisms.    De- 
ploys   it.       A    Sophism,    or    Sophistical   finitionofeach, 

reasoning,  is  a  faulty  argument  understood  by  him 
who  employs  it,  and  used  for  the  very  purpose  of 
deceiving.     It  is  is  proper  to  add,  how- 

Both  have   the 

ever,  that  these  distinctions  have  no  same  Logical 
logical,  whatever  may  be  their  moral  force' 
significance,  and  that  they  are  often  overlooked  by 
good  writers  who  use  the  terms  Fallacy,  Paralo- 
gism, and  Sophism  interchangeably  and  indiscrimi- 
nately. 

4.  Fallacies  are  further  divisible  into  Formal 
and  Material.     The  former  are  those 

,  .  ,  .  Formal  and  Ma- 

in Which  no  Conclusion  follows  from  the   terial  Fallacies 

premises,  however  there  may  be  an  ap-  disUnsuislie(L 
pearance  of  it.     These  are  all  cases  of  more  than 
three  terms,  Undistributed  Middle,  II-     Instances  of 
licit  Process,  Negative  Premises,  affirma-     ^ 
tive    conclusion    with    either    premise    negative,* 

*  It  is  important,  however,  to  remember  that  many  proposi- 
tions, in  form  negative,  are  not  so  in  the  fact,  because  the  force 
of  the  negative  particle  falls  on  the  subject  or  predicate  instead 
of  the  copula.     Propositions  are  in  reality  negative  only  when 


160  LOGIC.  [Chap.  VI. 

making  any  conclusion  from  particular  premises,  or 
a  universal  conclusion  when  either  premise  is  par- 
ticular, except  when  Substitutive  Judgments  furnish 
the  necessary  distribution  of  terms,*  from  denying 

the  real  import  of  the  copula  is  negative,  so  dividing  the  two 
terms  from  each  other.    Thus  : 

"  He  who  has  not  enough  is  not  really  rich, 
No  miser  has  enough, 
.*.  No  miser  is  really  rich." 

The  minor  premise  is  really  equivalent  to 

"  All  misers  are  persons  who  have  not  enough, 
.-.  All  misers  are  persons  not  really  rich." 

"  No  person  who  is  not  secure  is  happy, 

No  tyrant  is  secure  =  All  tyrants  are  persons  not  secure, 
.•.  No  tyrant  is  happy." 

Where  both  premises  are  really  negative  such  an  experiment  will 
not  succeed. 

"  Vicious  persons  are  not  happy, 
A  and  B  are  not  vicious, 
.*.  No  conclusion." 

All  attempts  to  transfer  the  negative  particle  to  one  of  the  terms 
here,  will  result  in  Four  Terms,  or  Undistributed  Middle,  or  in 
altering  the  meaning  of  one  premise. 
•  Such  an  exception  is  the  following: 

"  Some  mortals  are  (all)  men. 
Some  men  are  (all  the)  poets, 
.-.  All  the  poets  are  mortal." 


Sec.  I.]  FALLACIES.  161 

the  Antecedent  or  affirming  the  Consequent  of  a  con- 
ditional ;  and  from  violating  any  of  the  canons  of  in- 
ference in  Disjunctives  and  Dilemmas :  inferring  A 
from  A,  or  O  from  O,  by  conversion,  etc.,  etc.  These 
have  been  developed  already  under  Formal  Logic, 
and  belong  properly  to  it.  They  are  vices  in  the 
very  form  of  thinking,  whatever  be  the  premises  or 
conclusion.  They  do  not,  indeed,  belong  to  real 
thought,  but   only  to   the  counterfeits 

to  •  Why  introduced 

which  simulate  it.  They  enter  into  in  Applied 
Applied  Logic  only  as  principles  of  oglc' 
Formal  Logic  which  are  applied  to  detect  vices  in 
reasoning  about  matters  of  actual  being.  Indeed, 
they  would  hardly  need  to  be  introduced  here  at  all, 
were  they  always  put  in  such  phrase  as  to  be  palpa- 
ble. If  apparent,  the  invalidity  of  the  argument  in 
which  they  occur  is  self-evident.  They  are,  how- 
ever, very  apt  to  be  disguised  under 

,  .  ~       Often  disguised. 

equivocal  or  vague  expressions  ;  or,  tor 
other  reasons,  to  elude  the  notice  of  those  con- 
cerned.    On  this  account  they  require  to  be  noticed 
in  Applied  as  well  as  in  Formal  Logic. 

5.  Material  Fallacies  are  such  as  occur  when  there 
is  no  fault  in  the  reasoning  process,  and  Material  Falla. 
the  conclusion  does  follow  from  the  pre-  cies  Defined. 

14  *  L 


162  LOGIC.  [Chap.  VI. 

mises.     Hence  called  Material,  because  they  lie  not 

in  the  form,  but  the  matter  of  the  Syllogism.     Is 

it    asked,    how   is   a   fallacy    possible 

Groundless  pre- 
mise or  irrele-  here?     The  answer  is,  1st,  that  a  pre- 

vant  conclusion.        .  i  i  i  i 

mise  may  be  unwarrantably  assumed,  or 
2d,  the  conclusion  may  be  irrelevant.     It  may  fall 
short  of  what  the  reasoner  intends  or  professes  to 
I      atio        prove.     The  technical  name  of  this  lat- 
Eienchi.         ^er  js  Jgnoratio  Elmchi — ignorance  of 
the  proof  of  the    real  issue,  the  contradictory  of 
your  adversary's  proposition  which  you  undertake 
or  assume  to  demolish.     This  is  a  fallacy  of  very 
frequent  occurrence.     It  is  a  common  defense  of 
criminals  to  allege  that  they  were  insane ;  and  to 
attempt  to  prove  this  by  showing  that 
xamp  e         ^       acted   very   unreasonably !      But 
this  is  not  to  the  purpose,  for  if  it  were,  all  crimi- 
nals would  be  maniacs,  and  guilt  would  be  impos- 
sible.    So  it  is  a  frequent  and  wicked  practice  of 
this  fallacy  or  sophism,  to  arouse  the  passions  of  the 
tribunal  appealed  to  in  regard  to  the  atrocity  of  an 
imputed  offense,  instead  of  proving  it  to  have  been 
committed  by  the  accused. 

6.  To  this  head  may  be  referred  various  argu- 
ments which  logicians  have  been  accustomed  to  con- 


Sec.  I.]  FALLACIES.  163 

trast  with  argumentum  ad  rem,  i,  e.  to  the  point. 

Such  is  argumentum  ad  vereoundiam,  or  Argumentum  ad 

appealing  to  the  feelings  of  reverence   ., '  ,._ 

for  certain  persons  or  objects,  instead  of  am, 

proving  the  point  in  hand :  argumentum 

"  .     Adignorantiam, 

ad  ignorantiam,  assuming  that  your  posi- 
tion is  correct  unless  your  adversary  can  evince  the 
contrary :  or  it  is  sometimes  used  to  denote  any  sort 
of  sophism   which   imposes  on   men's 

7  j  Ad  populum. 

ignorance :    argumentum    ad    populum, 

which  is  very  much  akin,  being  addressed  to  the 

passions  and  prejudices  rather  than  the  intelligence 

of  the  people  ;  and  finally  argumentum 

'  .  Adhominem. 

ad  hommem,  an  appeal  to  the  practice, 
principles,  or  professions  of  an  adversary,  as  con- 
firmatory of  our  own  position  or  fatal  to  his. 

This  argument  is   legitimate  so  far  as  concerns 
an  adversary,  and  for  the  purpose  of 

,  ,        How  far  valid. 

silencing  him.  11  understood  to  be 
limited  to  this,  it  is  not  objectionable.  So  our 
Saviour  often  employed  it  to  silence  the  cavils  of 
the  Pharisees  and  other  adversaries.  It  is  illegiti- 
mate when  employed  as  if  it  established  any  propo- 
sition absolutely,  or  were  binding  upon  any  besides 
those  whose   personal  opinions  and  conduct  thus 


164  LOGIC.  [Chap.  VI. 

make  against  their  positions ;  or  even  upon  them, 
after  they  renounce  such  opinions  and  conduct. 

7.  The  other  sort  of  material  fallacy  by  the  un- 
warrantable assumption  of  a  premise,  has  some 
forms  that  have  been  signalized  by  corresponding 
names.     Chief  among  these  is, 

Petitio  Principii  or  begging  the  question,  which 
Petitio  Princi-  *s  ^ne  unwarrantable  virtual  assumption 
p11'  of  the  thing  to  be  proved,  or  of  that  by 

which  it  is  to  be  proved,  without  proving  it,  in  the 
course  of  the  argument.  Thus,  if  one  undertake  to 
show  that  a  given  tariff  will  be  beneficial  because  it 
will  promote  the  public  wealth,  without  proving 
this  latter,  he  perpetrates  a  petitio  principii.  The 
most  deceptive  form  of  this  fallacy  is, 

Arguing  in  a  circle — argumentum  in  circulo — in 
Arguing  in  a  which  the  conclusion  is  virtually  used 
Circle.  £0  prove  the  premise,  thus  going  in  a 

circle  which  returns  upon  itself,  from  premise  to 
conclusion  and  from  conclusion  to  premise.  To 
argue  that  certain  men  are  good  because  they  be- 
long to  an  excellent  party,  and  that  this  party 
is  excellent  because  it  includes  such  worthy  mem- 
bers, is  to  argue  in  a  circle.     Some  demonstrate 


Sec.  I.]  FALLACIES.  165 

the  immortality  of  the  soul  from  its  simplicity, 
and  then  its  simplicity  from  its  immortality. 

8.  Non  causa  pro  causa  assumes  that  to  be  a 
cause  which  is  not  a  cause.  Foremost  Non  cauga  0 
among  these  is  the  fallacy  of  post  hoc  causai 
ergo  propter  hoc,  taking  a  mere  antecedent  of  an 
event  to  be,  as  a  matter  of  course,  its  cause.  As  if, 
because  night  precedes  day,  it  were  therefore  the 
cause  of  day,  or  because  civil  war  in  the  United 
States  preceded  the  continental  war  between  Aus- 
tria, Prussia,  and  Italy,  it  were  therefore  the  cause 
of  that  war.* 

9.  An  assumption  analogous  to  this  is  the  taking 
of  non  tale  pro  tali,  assuming  a  resem-  Non  tale 
blance  without  proving  it.  Thus,  "  the  tali- 
season  is  favorable  to  apples  because  peaches  are 
abundant,"  implying  such  a  resemblance  between 
these  two  kinds  of  fruit,  and  the  requisites  to  their 
growth,  as  warrants  such  an  inference.     "All  other 

*  Notwithstanding  the  elaborate  efforts  of  Mill,  Brown,  and 
others  to  prove  that  cause  is  only  antecedent  or  invariable  ante- 
cedent, the  intuitive  judgment  of  the  human  race  is  well  voiced 
in  the  following  words  of  Cicero. 

"Causa  est  ea  quid  efficit  id  cujus  est  causa.  Non  sic  causa 
intelligi  debet,  ut,  quod  cuique  antecedat,  id  ei  causa  sit,  sed  quod 
cuique  efficienter  antecedat." — Quoted  in  Bowen's  Logic,  p.  306. 


166  LOGIC.  [Chap.  VI. 

religions  are  delusions.     Therefore  Christianity  is  a 
delusion." 


Sect.  II. — Fallacies  partly  formal  and  partly 

MATERIAL. 

10.  By  far  the  most  numerous  and  misleading 

Semi  -  Logical  class  of  Fallacies,  are  those  styled  by 
Fallacies.  Whateley   "semi-logical."     This  term 

has  been  criticized  as  absurd,  as  if  there  were  no 
conceivable  medium  between  a  Fallacy  purely 
The  term  Ex-  logical,  or  non-logical.  But  whatever 
plained.  may  ^e  g^  0f  £}ie  term,  he  employs  it 

to  denote  a  reality  which  no  other  term  adequately 
denotes.  It  denotes  the  class  of  Fallacies  arising 
from  the  ambiguous  use  of  terms  in  reasoning,  or  in 
the  syllogism. 

11.  An  Ambiguous  Term  is  equivalent  to  Two 

Terms;  consequently,  if  either  of  the 

An    Amoignous  x  J 

Term = Two       three  terms  of  a  syllogism  be  ambigu- 

Terms 

ous,  it  amounts  to  bringing  a  fourth 
term  into  it.  But  when  there  are  four  terms  there 
can  be  no  conclusion.     We  see  then  how  this  Fal- 

How  Semi-Log-  lacy  of  Ambiguous  Terms  is  partly 
ical-  material  and  partly  formal.     In  order 

to  detect  the  ambiguity,  we  have  to  look  at  the 


Sec.  II.]  FALLACIES.  167 

matter  of  the  syllogism  as  contained  in  the  meaning 
of  its  terms.  So  far  it  is  material.  When  the  am- 
biguity is  detected,  the  fault  which  gives  rise  to  the 
fallacy,  is  shown  at  once  to  be  formal,  because  the 
syllogism  is  loaded  with  four  terms  which  are  in- 
compatible with  any  conclusion.  It  is  true  that,  at 
bottom  and  in  essence,  this  fallacy  is  formal.  But 
the  discovery  of  it  requires  examination  of  the  mat- 
ter embraced  in  the  syllogism.     Thus : 

"  Feathers  are  light, 
Light  is  contrary  to  darkness, 
.'.  Feathers  are  contrary  to  darkness," 

is  a  syllogism  in  reality  with  four  terms,  two  of 
which  are  words  spelt  with  the  same  letters,  but  of 
different  meanings.  This  difference  of  meaning 
must  be  ascertained  in  order  to  expose  the  fal- 
lacy. 

12.  Fallacies  of  this  description  are  far  the  most 
specious  and  numerous  of  all,  and  are  guc]1  Fanacies 
as  various  as  the  various  causes  or  kinds  sPecious< 
of  ambiguity  in  language.  We  will  call  attention 
to  a  few  of  the  more  prominent  that  logicians  have 
been  accustomed  specially  to  designate. 


168  LOGIC.  [Chap.  VI. 

13.  The  fallacy  of  Division  and  Composition. 
Division  and  ^n  tms  the  middle  term  is  taken  divi- 
Composition.  dedly  or  distributively  in  one  premise, 
and  collectively  in  the  other.     Thus : 

"All  these  persons  are  a  crowd, 
A.  and  B.  are  some  of  these  persons, 
.".  They  are  a  crowd." 

Here  persons  are  taken  collectively  in  the  major, 
and  distributively  in  the  minor. 

"  Five  is  one  number, 
Three  and  two  are  five. 
.\  They  are  one  number." 

This  is  composition  in  the  major  and  division  in 
the  minor. 

14.  This  fallacy  is  of  constant  occurrence  in  con- 
Paliacy  of  the  action  with  the  word  "  all,"  which,  in 
word  all."  fae  peculiar  idiom  of  our  language, 
affords  great  facilities  for  it.  First,  as  in  the  ex- 
amples given  above; 

"  All  these  soldiers  are  an  armv, 
All  these  soldiers  are  individual  persons, 
.*.  Individual  persons  are  an  army." 

Here  in  the  major  "all"  is  taken  collectively,  in 
the  minor  distributivelv. 


Sec.  II.]  FALLACIES.  169 

But  the  greatest  liability  to  an  ambiguous  or 
non-natural  sense  of  the  word  "  all,"  is 
where  it  is  the  subject  of  a  negative 
judgment,  in  which  case  it  is  nevertheless  impossi- 
ble to   deny  the  predicate  of  "all"   the   subject. 

Thus : 

"  Not  all  men  are  poets,  or 

All  men  are  not  poets," 

is  equivalent  to 

"  Not  every  man  is  a  poet,  or 
Some  men  are  not  poets." 

Sometimes  there  is  danger  of  construing  "  not  all"  as 
equivalent  to  none,  whereas  it  only  amounts  to 
"  not  some."  This  is  well  illustrated  by  Whateley 
in  the  following  example : 

"  If  all  testimony  to  miracles  is  to  be  admitted,  the  Popish 
legends  are  to  be  believed ;  but  the  Popish  legends  are  not  to 
be  believed ;  therefore  no  (for  "  not  all")  testimony  to  miracles 
is  to  be  admitted." 

It  is  important  to  be  on  our  guard  against  fallacies 
arising  from  ambiguities  in  this  pregnant  mono- 
syllable. 

15.  A  very  ensnaring  form  of  ambiguous  middle 
is    known   as   Fallacia  Accidentis.   or  , 

Fallacia  Acci- 
a  clieto  secundum  quid  ad   dictum  sim-    dentis. 

15 


170  LOGIC.  [Chap.  VI. 

pliciter,  and  vice  versa,  i.  e.  of  using  the  middle 
term  considered  with  reference  to  some  of  its  acci- 
dents in  one  premise,  and  with  reference  to  its  mere 
essence  in  the  other. 

"  The  covering  of  sheep  is  what  we  wear, 
Undressed  wool  is  the  covering  of  sheep, 
.*.  Undressed  wool  is  what  we  wear." 

Again : 

"  Government  is  a  blessing, 

The  most  cruel  despotism  is  a  government, 
.".  Therefore  it  is  a  blessing." 

16.  A  very  common   form  of  ambiguous  mid- 

Paiiacy  of  Ety-  dle  is  that  founded  on  Etymology,  or 
mology.  the  assumption   that   derivative,  paro- 

nymous,  or  conjugate  words  have  the  signification 
of  their  roots,  and  compounds  of  their  originals.  It 
is  true  indeed,  that  the  meaning  of  words  sometimes 
remains  unchanged  through  all  these  variations. 
Sometimes  the  changes  of  meaning  are  slight,  but, 
for  that  very  reason,  all  the  more  liable  to  be  over- 
looked and  to  gender  fallacies.     Thus : 

"  Projectors  ought  not  to  be  trusted, 

This  man  has  formed  a  project, 
.*.  He  ought  not  to  be  trusted." 


Sec.  II.]  FALLACIES.  171 

"  Artful  persons  should  be  shunned, 
A.  B.  is  a  great  artist, 
.'.  He  ought  to  be  shunned." 

"  Truth  is  derived  from  to  trow,  i.  e.  believe, 
But  belief  is  variable, 
/.  Truth  is  variable,  i.  e.  not  immutable." 

17.  Analogous  to  this  is  the  Fallacy  of  Interro- 
gations, sometimes  called  Fallacia  Plu-  pailacy  of  In_ 
rium  Interrogationum.  This  is  prac-  terrogations. 
ticed  when,  under  one  question  in  form,  by  ambi- 
guity of  meaning,  more  than  one  question  in  reality 
is  put,  so  that  the  person  questioned  is  entrapped, 
whatever  answer  he  may  give.  This  is  a  trick  fre- 
quently practiced  by  examiners  of  witnesses.  Law- 
yers are  peculiarly  prone  to  it.  They  put  ambigu- 
ous and  embarrassing  questions,  and  then  with 
great  show  of  sincerity  and  fairness,  insist  on  a 
categorical  yes  or  no  for  answer,  as  if  to  refuse  such 
an  answer  would  imply  a  lack  of  truthfulness,  when 
in  fact,  such  a  categorical  answer  must  be  false  or 
inadequate,  owing  to  the  ambiguous  implications  of 
the  interrogation. 

So  the  attempt  is  often  made  to  ensnare  or  deceive, 
by  a  false  assertion  or  implication,  in  a  False  impiica- 
question  so  put  as  to  imply  that  it  is    tioI1S, 


172  LOGIC.  [Chap.  VI. 

beyond  dispute.     No  better  instance  of  this  can  be 

found  than  the  celebrated  question  of  Charles  II.  to 

the  Royal  Society,  "Why  a  dead  fish 

xamp  (  ^oeg  ^^  though  a  live  fish  does,  add  to 

the  weight  of  a  vessel  of  water  in  which  it  is  placed  ?" 
This  was  put  with  such  apparent  assurance  that 
some  of  the  philosophers  were,  for  the  time,  de- 
ceived, and  busied  themselves  in  seeking  an  expla- 
nation of  the  fact,  while  they  omitted  to  inquire  if 
it  was  a  fact.  So,  many  an  innocent  person  has  been 
entangled  and  led  to  criminate  himself,  being  for  the 
moment  unmanned  and  thrown  off  his  guard,  by  the 
very  audacity  with  which  such  questions  were  put  to 
him  as  these :  "  How  long  since  you  left  off  drinking, 
swearing,  back-biting,"  etc.  ?  No  duty  is  more  in- 
cumbent on  courts  than  that  of  protecting  witnesses 
and  parties  against  such  injustice. 

18.  Quite  similar  to  this  is  the  demand  often 
_     _,     made  upon  witnesses  by  examiners,  not 

Demand  for  Dis-  x 

tract  and  Ade-  only  for  a  Clear,  but  for  a  Distinct  and 

qnate Cognition.  .   ,  ^         ...        ,  -.  T-r 

even  Adequate  Cognition  (see  chap.  II., 

Sects.  9,  30)  implying  that  their  testimony  is  to  be 

suspected,  unless,  besides  certainty  as  to  the  object 

testified  about,  they  can  also  give  its 
Example. 

marks.     Thus,  if  a  witness  testifies  that 


Sec.  II.]  FALLACIES.  173 

a  certain  signature  or  manuscript  is  in  a  given  man's 
hand-writing,  it  is  quite  common  to  insist  that  he 
should  give  some  of  the  marks  or  distinctive  pecu- 
liarities by  which  he  distinguishes  the  chirography 
in  question.  The  same  thing  is  often  done  in  ex- 
aminations for  the  purpose  of  identifying  persons, 
places,  and  other  objects.  The  fallacy  of  all  this, 
so  far  as  it  implies  distrust  of  the  testimony  of  those 
who  are  unable  to  give  the  marks,  is  palpable.  In 
general  it  is  only  the  few  experts,  in  each  panacy  ^. 
department,  who,  besides  knowing  ob-  Posedi 
jects  with  certainty,  can  give  the  distinguishing 
marks  or  definitions  of  them.  There  are  few  things 
that  we  know  with  more  certainty  than  the  different 
hand-writings  with  which  we  have  been  familiar. 
There  are  few  matters  in  respect  to  which  those  who 
have  not  made  it  a  subject  of  special  study,  will 
more  certainly  and  egregiously  blunder,  than  in  at- 
tempting to  give  the  marks  which  distinguish  the 
chirography  of  different  persons.  So  with  other 
things.  Nothing  would  sooner  nonplus  such  ques- 
tioners themselves  than  to  exact  of  them  a  logical 
definition  of  words,  or  the  marks  of  conceptions,  with 
which  they  are  perfectly  familiar,  and  which  they 
constantly  use  with  substantial  accuracy. 

15* 


174  LOGIC.  [Chap.  VI. 

19.  Another  fallacy  is  the  Over-estimation  of 
Probabilities,  i.  e.  of  the  degree  of  belief  which 

Over-estimation  ought  to  be  produced  by  evidence  less 
of  Probabilities,  than   certain — especially   of  supposing 

that  a  plurality  of  probabilities  necessarily  strengthen 

each  other.     A  single  probability  of  any  uncertain 

event  is  ascertained  by  dividing  the  number  of  chances 

favorable  to  the  event  by  the  total  number  of  chances. 

Thus  the  probability  that  a  person  blindfolded  will 

take  a  black  ball  out  of  an  urn  containing  10  white 

and  2  black  balls  is  yi  or  h 

20.  "  To  find  the  chance  of  the  recurrence  of  an 
event  already  observed,  divide  the  number  of  times 
the  event  has  been  observed,  increased  by  one,  by  the 
same  number  increased  by  two.  If  an  inlander  coming 
to  the  sea,  observed  the  phenomenon  of  the  tide 
ten  times  in  succession,  the  chance  to  him  that  at 
the  next  period  the  tide  would  again  rise  would  be 
T¥+i==ir^  or  11  to  1.  Every  certainty  is  repre- 
sented by  a  unit,  as  has  been  shown ;  and  so  many 
units  are  added  to  the  possible  cases  (denominator 
of  the  fraction)  as  there  have  been  events,  and  so 
many  to  the  favorable  cases  (numerator)  as  there 
have  been  favorable  events.  '  Or,  if  we  represent/ 
says  M.  Quetelet,  'the  number  of  times  that  the 


Sec.  II.]  FALLACIES.  175 

event  has  occurred  by  a  similar  number  of  white 
balls  that  we  throw  into  an  urn,  adding  also  one 
other  white  ball  and  one  black  ball,  the  probability 
of  the  reproduction  will  be  equal  to  that  of  drawing 
a  white  ball.' 

"In  order  to  calculate  the  probability  that  an 
event  already  observed  will  be  repeated  any  given 
number  of  times,  the  rule  is,  to  divide  the  number  of 
times  the  event  has  been  observed,  increased  by  one, 
by  the  same  number  increased  by  one  and  the  number 
of  times  the  event  is  to  recur.  Thus,  if  the  tide  had 
been  observed  9  times,  the  chance  that  it  would  re- 
cur ten  times  more  would  bef4.10;j;T  = (-j-J)  =  %. 
'  This  is  the  same  thing  as  if  each  reproduction  of 
the  observed  event  corresponded  to  putting  a  white 
ball  in  an  urn  where  there  were  already,  before 
commencing  the  trials,  a  white  ball  and  as  many 
black  balls  as  it  is  supposed  that  the  event  observed 
should  re-occur  times/  " — Thomson' sLaws  of  Thought. 

21.  If  two  or  more  probabilities  are  independent 
of  each  other,  they  do  afford  mutual  -^j^w 
support.     But  if  otherwise,  if  they  are  strengthen  and 

when  they 

probabilities  of  probabilities,  they  weak-  weaken  each 
en  each  other.    .If  the  credibility  of  a  other" 
witness  be  f  so  far  as  his  ability  to  observe  aright 


176  LOGIC.  [Chap.  VI. 

and  know  the  facts  is  concerned,  f  so  far  as  his 
veracity  is  concerned,  then  the  total  probability  of 
his  telling  the  truth  is  §  X  f  =  A,  unity  being  the 
representative  of  certainty. 

22.  If,  however,  the  probabilities  are  mutually 
independent,  they  strengthen  each  other,  and  as 
they  increase  in  number  and  force,  they  may  come 
short  of  certainty  by  only  an  infinitesimal  distance. 
Thus,  if  the  probability  that  A.  B.  committed  a 
given  murder  be  strong,  1,  from  certain  money  be- 
longing to  the  victim  being  found  in  his  possession ; 
2,  from  his  boots  fitting  tracks  found  near  the 
place  of  murder;  3,  from  blood  on  his  clothes; 
4,  from  a  piece  of  knife-blade  found  in  the  head  of 
the  murdered  body  fitting  precisely  the  broken 
blade  of  a  bloody  knife  found  in  the  pocket  of  the 
suspected  person ;  it  is  clear  that  all  these  separate 
probabilities  confirm  each  other,  and  together  fall 
only  short  of  apodictic  proof.  In  this  case,  the  mode 
of  computing  the  absolute  probability,  is  to  sub- 
tract each  separate  probability  from  unity,  which 
gives  the  probability  of  the  opposite  event,  or  of 
failure  arising  from  each  several  cause.  But  as  these 
several  probabilities  of  the  opposite  event  weaken 
each  other,  or  are  probabilities  of  probabilities,  the 


Sec.  II.]  FALLACIES.  177 

entire  probability  of  it  is  ascertained  by  multiply- 
ing the  separate  ones  together.  This  product  sub- 
tracted from  unity  will  give  the  probability  of  the 
original  event  in  question,  of  which  this  is  the  oppo- 
site.* Thus  in  the  example  just  given  j  let  the 
first  probability  be  \,  the  second  \y  the  third  \y  the 
fourth  J.  Subtracting  each  of  these  from  unity, 
and  multiplying  them  together,  we  have  iXf XfX 
\  =  ■£$  =  j3g-,  which,  subtracted  from  1,  gives  -^f ,  as 
the  probability  that  the  suspected  person  was  the 
real  murderer — a  probability  sufficient  to  neutralize 
all  reasonable  and  practical  doubt. 

23.  Strictly,  however,  this  and  all  positive  direc- 
tions touching:  the  calculation  of  proba-  _  .  ,  ,  , 

0  x  Strictly  belongs 

bilities,  belong  to  the  doctrine  of  Me-  to  Logical  Me- 
thod.    It  comes  in  here  very  naturally, 
however,  in  connection  with  the  correlate  fallacy. 

*  "  As,  in  the  case  of  two  probable  premises,  the  conclusion  is 
not  established  except  on  the  supposition  of  their  both  being  true, 
so  in  the  case  of  two  (and  the  like  holds  good  with  any  number) 
distinct  and  independent  indications  of  the  truth  of  some  propo- 
sition, unless  both  of  them  fail,  the  proposition  must  be  true  ;  we 
therefore  multiply  together  the  fractions  indicating  the  proba- 
bility of  failure  of  each, — the  chances  against  it;  and  the  result 
being  the  total  chances  against  the  establishment  of  the  conclu- 
sion by  these  arguments,  this  fraction  being  deducted  from  unity, 
the  remainder  gives  the  probability  for  it." — Whatcley's  Logic, 

Book  III.,  15. 

M 


178  LOGIC.  [Chap.  VI. 

24.  A   source   of   ambiguity,   not   only   in   the 

middle,  but  other  terms,  which  ought 

Ambiguity  Pic-  J  '  & 

tae  Universaii-  not  to  be  overlooked,  although  the 
means  of  guarding  against  it,  will  more 
fully  appear  under  the  head  of  Induction,  has  re- 
ceived the  name  fictce  universalitatis  /.  L  e.  of  a 
groundless  inference  from  a  few  cases  to  all  cases. 
This  is  among  the  most  common  forms  of  delusive 
and  fallacious  reasoning.  Common  Ex- 
amples of  this  are,  that  Friday  is  an 
unlucky  day,  because  some  enterprises  begun  on  that 
day  have  suffered  disaster:  that  an  epidemic  is 
raging,  when  only  the  fewest  cases  of  disease  have 
appeared  :  that  hemorrhage  of  the  lungs  is  always 
fatal,  because  it  is  often  so :  that  all  men  are  knaves 
because  so  many  are :  that  the  whole  community  are 
of  a  given  opinion,  because  A.  B.  and  C.  have  ex- 
pressed it.  Out  of  such  fictitious  universals  arise 
Syllogisms  like  the  following : 

"  Men  love  to  be  humbugged, 
The  President  of  the  Bible  Society  is  a  man, 
.'.  He  loves  to  be  humbugged." 

25.  The  sources   of  ambiguous   middle  are  as 

numerous  and  varied  as  the  sources  of 

Sources  of  Am- 
biguous Middle,  ambiguity  in  language  itself.    Their  de- 


Sec.  III.]  FALLACIES.  179 

tection  and  correction  belongs  rather  to  rhetoric, 
grammar,  or  philology,  than  to  logic.  We  have  no 
room  to  pursue  it  further  here.  Those  who  desire 
to  see  it  unfolded  at  greater  length,  may  consult  the 
chapter  on  Fallacies  in  Whateley's  Logic  with  in- 
terest and  profit. 

26.  It  only  remains  that  in  concluding  the  sub- 
ject of  Fallacies  we  present  some  specimens  of 

Sect.  III. — Logical  Puzzles. 
In  inventing  which  the  intellectual  activity  of 
past   times   exerted  itself,  for  lack  of 

Logical  Puzzles 

worthier  objects.     These  have  been  be-  more  ingenious 

■  it  -. .  ,  •  ,      than  useful. 

queathed  to  succeeding  generations  to 
task  their  subtlety,  and  at  once  amuse  and  perplex 
students  in  their  leisure  hours.  This  however  has 
not  been  the  worst  of  it.  They  have  gone  far  to 
countenance  the  impression  that  Logic,  instead  -of 
being  a  genuine  or  useful  science,  is  little  better 
than  a  kind  of  jugglery  and  legerdemain,  for  work- 
ing up  seeming  demonstrations  of  manifest  absurdity 
and  falsehood. 

27.  The  Dilemma  is  a  favorite  instru- 

.  Use  of  the  Di- 

luent for  this  sort  of  logical  sleight  of  lemma  for  this 

hand.     A  sly  fault  in  some  member  of  purpoi 


180  LOGIC.  [Chap.  VI. 

its  complex  parts  affords  the  facile  opportunity  for 
it,  because  it  is  so  readily  unobserved.  The  standard 
examples  we  are  about  to  quote  from  the  books,  will 
illustrate  this. 

28.  "  In  sifting  a  proposed  Dilemma,"  says  Krug, 
"we  are  to  look  closely  to  the  three 

Krug's  rules  for 

sifting  Dilem-  following  particulars  : — 1.  Whether,  in 
the  Sumption,*  the  Consequent  is  a  legi- 
timate inference  from  the  Antecedent ;  2.  Whether 
the  Disjunction  in  the  Consequent  is  complete ;  3. 
Whether,  in  the  Subsumption,f  the  Disjunct  Mem- 
bers are  properly  sublated.  The  following  Dilemma 
is  faulty  in  each  of  these  respects. 

"  If  Philosophy  be  of  any  value,  it  must  procure  for  us  power, 
riches,  or  honor. 

"  But  it  procures  neither  of  them.     Therefore,"  etc. 

"  Here,  1,  the  inference  is  wrong,  as  Philosophy 
may  be  worth  something,  though  it  does 

Solution.  ,  p  ,,  .      , 

not  secure  any  ot  these  external  advan- 
tages; 2,  the  Disjunction  is  incomplete,  as  there  are 
other  goods,  besides  the  three  here  enumerated ; 
3,  the  Subsumption  is  false,  as  Philosophy  has  often 
been  the  means  of  procuring  these  very  advantages." 

*  Major  premise.  f  Minor  premise. 


Sec.  III.]  FALLACIES.  181 

29.  Analogous  to  this  is  the  old  quibble  to  dis- 
prove the  possibility  of  motion,  which  Puzzle  about 
also  throws  up  the  horns  of  a  dilemma.  Motion' 
Thus : 

"  If  Motion  is  possible,  a  body  must  move  either  in  the  place 
where  it  is,  or  in  a  place  where  it  is  not. 

"  But  a  body  cannot  move  in  a  place  where  it  is ;  and  of  course, 
it  cannot  move  where  it  is  not. 

"  Therefore,  motion  is  impossible." 

The  Major  Premise  or  Sumption  is  false  and  in- 
volves a  Material  Fallacy.  The  true 
statement  is  that,  if  motion  is  possible, 
a  body  must  move  from  the  place  where  it  is  to 
a  place  where  it  will  be.  This  removes  every  ap- 
pearance of  a  puzzle.  The  Major  Premise  is  false 
except  with  regard  to  one  indivisible  moment.  But 
that  is  irrelevant  to  motion,  which  in  its  nature  re- 
quires time,  while  the  cognition  of  it  supposes 
memory. 

30.  To  the  same  complexion  comes  the  famous 
old  Puzzle  named  Ignava  Ratio,  i.  e.  the 

,  '«       .         ..  i  Ignava  Ratio. 

argument  for  inaction,  because  events 

being  predetermined  or  otherwise  fixed,  all  effort  to 

alter  them,  or  to  attain  what  is  desirable  and  avert 

16 


182  LOGIC.  [Chap.  VI. 

what  is  evil,  is  unavailing.     Cicero  thus  states  it  as 
urged  against  calling  in  medical  aid  in  sickness : 

"  If  it  is  fated  that  you  shall  recover  from  the  present  dis- 
ease, then  you  will  recover  whether  you  call  in  a  physician  or 
not.  If  it  is  fated  that  you  shall  not  recover,  then,  with  or 
without  a  physician,  you  will  not  recover. 

"  But  either  the  one  or  the  other  of  these  is  fated. 

"  Therefore,  it  will  be  of  no  use  to  call  in  a  doctor." 

The  obvious  fallacy  here,  to  look  no  deeper,  lies 
in  the  fact,  that  the  calling  in  of  the  doctor  and 
using  his  prescriptions,  may  be  the  very  means  by 
which  it  is  ordered  that  recovery  shall  take  place; 
hence  the  first  member  of  the  sumption  or  major 
premise  is  false.     And  so  of  all  analogous  cases. 

31.  The  famous  puzzle  of  Achilles  and  the  tor- 

Aohfflesandthe  toise>  which    S0    long  baffled   tne   1(>gi- 
tortoise.  cians,  aiming   to   prove,  by  logic,  the 

logical  absurdity,  that  the  swiftest  runner  can  never 

overtake  the  slowest,  is  put  thus : 

"  The  swiftest  runner  can  never  overtake  the  slowest,  if  the 
latter  has  ever  so  little  a  start.  Suppose,  for  instance,  that 
Achilles  runs  ten  times  as  fast  as  a  tortoise,  and  that  the  tor- 
toise is  one  mile  in  advance  at  the  outset.  While  Achilles  is 
traversing  this  mile,  the  tortoise  has  advanced  y^th  of  a  mile 
farther ;  before  his  pursuer  has  passed  over  this  TVth,  the  tor- 
toise has  advanced  j^th,  and  then,  again,  xsWth,  and  so  on 


Sec.  III.]  FALLACIES.  183 

forever,  always  being  some  fraction,  however  small,  of  a  mile  in 
advance." 

The  sophism  here  is  disguised  under  a  false  state- 
ment of  the  problem.  The  real  ques-  The R  ..^ 
tion,  when  will  Achilles  overtake  the  exposed. 
tortoise  ?  is  kept  out  of  sight,  and  another  wholly 
different  substituted  in  its  place,  viz.,  when  the 
tortoise  is  at  any  given  point  ahead  of  Achilles, 
how  far  will  it  have  gone  when  Achilles  shall  reach 
that  point  ?  This  soon  runs  into  infinitesmals  which 
are  practical  zeros,  and,  even  if  theoretically  infinite 
in  number,  really  are  all  included  in  that  finite  length 
which  Achilles  will  quickly  get  over,  leaving  the 
tortoise  behind. 

32.  Other  puzzles  abound  on  which  we  have  no 
room  to  dwell.     It  is  the  less  necessary, 

*         Such  puzzles 

as  a  careful  application  of  the  principles  have  no  chief 
already  laid  down,  will  readily  solve  pac<m  °S1C' 
them.  The  propounding  and  solution  of  such 
quibbles  may  be  a  casual  diversion,  it  cannot  be  a 
principal  object  of  pursuit,  in  any  science  worth 
serious  study. 


CHAPTER  VII. 


LOGICAL   METHOD. 


1.  Method,  ftsdbdoz,  is  the  way  by  which  we  pro- 
ceed to  a  given  goal.     Logical  Method 

Method  Defined.    .     .,  n         -,    .         ,-,  •      •    1         /? 

is  the  way  of  applying  the  principles  ot 
Logic  to  the  discovery,  confirmation,  or  elucidation 
of  the  truth. 

In   order   to   this,  it  is  necessary  to  determine 

the  sphere  and  matter,  the  extension 

vSoT  SDefini-  an(^  intension,  the  objects  and  thequal- 
tion,  and  Kea-  [t[e^  with  which  we  have  to  do.  The 
former  is  accomplished  by  Logical  Divi- 
sion, and  the  latter  by  Definition,  which  have  been 
duly  treated  in  their  respective  places,  in  the  Chap- 
ter on  Conceptions.  To  this  we  refer  the  student 
as  sufficient  for  present  purposes,  while  we  pass  to 
consider  more  especially  the  use  of  Reasoning  in 
the  search  and  proof  of  truth. 

184 


Sec.  I.]  METHOD.  ^5 

2.  It  must  not  be  forgotten  that  Logic  does  not 
give  us  the  original  facts,  axioms,  or  T    . 

0  °  '  Logic   not    the 

first   principles,   which   constitute    the  Original  source 

-tir*  of  Knowledge. 

primary  matter  or  groundwork  01  our 
knowledge.  These  are  furnished  by  Its  sources  enu. 
Intuition,  either  1.  Of  the  phenomena  merated- 
of  consciousness,  i.  e.  psychological  facts :  or  2.  By 
sense-perceptions,  i.  e.  of  facts  pertaining  to  the 
material  and  external  world — or,  3.  By  supersensual 
intuitive  truths,  i.  e.  self-evident  axioms :  or  finally, 
by  testimony  either  spoken  or  recorded.  _    T    . 

*  *  How  Logic  deals 

Logic  deals  with  the  matter  thus  af-  with  the  matter 

n     i    i    •  .  r>ii  -iT;iso  furnished. 

lorded  in  a  two-iold  way.  1.  In  the 
application  of  its  principles  to  test  and  explicate 
what  is  contained  implicitly  in  the  matter  so  fur- 
nished by  the  intuitive  faculties :  2.  By  guiding  us 
in  such  use  of  our  intuitive  faculties,  as  shall  be  most 
effective  for  advancing  our  knowledge.  According 
to  the  former,  the  laws  of  Conceptions,  Judgments, 
and  Reasonings  show  what  is,  and  what  is  not,  ne- 
cessarily implied  by  the  facts  and  truths  given  us 
from  other  sources.  In  the  latter,  it  helps  to  guide 
our  inquiries,  observations,  and  experiments  towards 
the  search  for  and  intuition  of  such  facts  as  will 
tend  to  elucidate  or  decide  questions  in  issue,  thus 

16* 


186  LOGIC.  [Chap.  VII. 

saving  us  the  waste  of  our  powers  in  irrelevant  and 
fruitless  investigations. 

Section  I. — Original  and  Derivative  Sources  op 

Knowledge. 

3.  Our  Original  Sources  of  Knowledge  then  are  the 
Intuitive  (including  Self-Consciousness, 

Recapitulation 

of  sources  of  Sense-Perception,  Self-Evident,  Super- 
sensual  truths),  and  Testimony.  The 
Derivative  are  what  we  derive  from  them  through 
the  power  of  Discursive  Thought,  including  Ab- 
straction, Generalization,  Conception,  Judgment, 
Reasoning.  Some  add  to  these  Memory, 
of  whom  some  class  it  with  the  former 
faculties,  some  with  the  latter.  It  is  unnecessary  to 
discuss  this  question  here.  It  is  enough  that  Me- 
mory is  not  itself  a  direct  source  of  knowledge  in- 
tuitive or  discursive.  It  simply  keeps  and  repro- 
duces what  is  known  through  the  other  faculties. 
Some  questions  too  might  arise,  as  to  how  far  Testi- 
mony is  an  intuitive,  or  immediate  source  of  know- 
ledge. It  is  not  our  plan  here  to  go  far  in  the 
discussion  of  such  extra-logical  questions.  They 
are  to  be  relegated  to  psychology,  except  so  far  as 
may  be  essential  to  a  due  understanding  of  Logic  or 


Sec.  I.]  METHOD.  187 

its  applications.  It  suffices  for  our  present  purpose 
that  Memory,  like  the  intuitive  faculties,  furnishes, 
inasmuch  as  it  preserves,  material  for  the  discursive 
faculties,  but  is  not  itself  discursive. 

4.  Memory  is  an  essential  element  in  nearly  all 
Testimony.     It  is   rare   that   any  one 

Memory        in- 

bears  witness  simply  to  the  cognitions  volved  in  Testi- 
of  the  present  moment.     Almost  all  tes-       y' 
timony  respects  the  past. 

5.  Testimony  is  a  fundamental  source  of  know- 
ledge. All  facts  known  to  us  beyond  imp0rtance  0f 
the  narrow  circle  of  our  own  experience,  Testlm°Qy' 
must  be  learned  from  Testimony.  And  our  gene- 
ralizations and  reasonings  would  be  extremely  scanty 
for  lack  of  material,  without  the  results  of  the  ex- 
perience of  other  men,  added  to  our  own,  and  au- 
thentically reported  to  us. 

Testimony  may  be  either  Oral,  or  Recorded  in 
historical  writings,  monuments,  memen-  0ral  and  Ee- 
toes,  and  tokens.  The  canons  for  dis-  corded« 
tinguishing  true  testimony  from  false,  and  genuine 
from  spurious,  authentic  from  fictitious  history,  are 
manifold  and  easily  accessible.  To  discuss  them 
is  aside  of  our  present  purpose  and  beyond  our 
space. 


188  LOGIC.  [Chap.  VII. 

6.  There  is,  however,  one  species  of  testimony 

that  is  wholly  unique,  and  above  the 
God  in  his  Word  plane  of  all  human  witnessing.      We 

refer  to  the  testimony  of  God  in  his 
Word.  This  is  absolutely  sure  and  infallible,  be- 
ing the  utterance  of  Him  for  whom  it  is  impossible 
to  err  or  to  lie.  It  is  the  exclusive  source  and 
foundation  of  Christian  Theology.  It  is  absolutely 
true  and  authoritative.  To  unfold  the  rules  for 
the  correct  interpretation  of  Scripture  would  be  to 
trench  on  the  sphere  of  exegetical  theology. 

7.  It  is  proper,  however,  to  remark  that  the  first 

Theolo  fo  nd-  Pr^nc^P^es  °f  theology  do  not  depend 
ed  on  the  an-  upon  any  process  of  reasoning,  a  priori 
or  inductive,  but  upon  the  authority  of 
God  who  declares  them.  In  a  qualified  sense,  the 
true  process  for  ascertaining  what  the  Scriptures 
teach  may  be  viewed  as  inductive.  In  other  words, 
it  simply  ascertains  and  compares  the  actual  teach- 
ings of  Scripture,  instead  of  deciding  a  priori  what 
they  may  and  may  not  teach. 

8.  The  application  of  the  laws  of  thought  or  prin- 
m,     ,         „     ciples  of  logic  to  the  facts,  that  are  al- 

The  laws   of  x  °  ' 

thought  always  ways  coming  before  us  in  an  isolated 
and   unorganized    form,   is   constantly 


Sec.  I.]  METHOD.  189 

made,  consciously  or  unconsciously,  by  all  men. 
The  power  to  do  it  is  one  of  man's  chief  preroga- 
tives as  compared  with  the  brutes.  To  think  at  all 
is,  either  consciously  or  unawares,  to  conform  to  the 
laws  of  thought.    All  else  called  think- 

Unlogical   is 

ing  only  simulates  and  counterfeits  it.  counterfeit 
But,  in  proportion  as  this  application  ous  fe 
of  the  principles  of  logic  becomes  comprehensive 
and  complete,  in  regard  to  any  given  department 
of  facts  or  truths,  it  becomes  a  scientific  view  of 
them.  Thus,  a  comprehension  of  the  facts  con- 
cerning life,  in  their  mutual  relations,  their  har- 
mony and  unity  according  to  the  necessary  laws  of 
thought,  makes  up  the  science  of  Physiology ;  of 
the  phenomena  of  the  soul,  Psychology ;  of  spatial 
quantity  and  relations,  Geometry. 

9.  Science  then  is  not  a  mere  knowledge  of  dis- 
jointed unreconciled  facts  or  truths,  but  gcience  what  it 
a  knowledge  of  these  facts  as  mutually  is* 
related,  harmonized,  and  unified,  under   all-inclu- 
sive principles  and  laws.     But,  in   the  sphere  of 
actual  being,  of  events  or  phenomena,  To  find  lawg  . 
to  ascertain  their  laws  and  principles  is  t0  find  causes. 
commonly  to  ascertain*  their  causes.     Towards  this 
state  all  knowledge  tends  in  proportion  as  it  tends 


190  LOGIC.  [Chap.  VII. 

to  perfection.    And  this,  not  only  in  each  particu- 
lar  department  of  inquiry  considered 

Perfect  know- 
ledge is  scien-    by  itself,  but  in  the  relation  of  them  all 

to  each  other.  They  are  more  and  more 
comprehended  in  their  mutual  relations  and  har- 
mony, until  they  culminate  in  absolute  unity  in  the 
Great  First  Cause,  and  the  Infinite  Mind. 

10.  This  process  is  actually  going  forward  with 
All  Sciences  grea^  rapidity  as  science  advances.  The 
tend  to  Unity,  various  Physical  Sciences  are  more  and 
more  seen  as  distinct,  yet  cognate  and  harmonious, 
divisions  of  one  great  whole.  The  same  is  true  of 
the  various  branches  of  Psychology  and  Metaphy- 
sics, in  their  mutual  coherence  and  interdependence: 
while  Physics  have  their  deepest  ground  in  Meta- 
physics, in  the  ideas  of  substance  and  cause,  with- 
out which  all  being  is  a  chimera,  and  all  science  a 

dream.     So  the  several  sciences,  physical 

Scientia   Scien-         ,         ,      ,       .     ,  .-, 

tiamm:  Philo-  and  metaphysical,  are  constantly  verging 
sophy  and  Onto-  towards  that  scientia  scientiarum,  which 

logy. 

is  at  once  the  true  Philosophy  and  the 
true  Ontology. 

11.  Philosophy  and  Science  have  been  used  very 
much  interchangeably,  and  very  much  also  in  more 
or  less  contrast  to  each  other.     In  the  former  case 


Sec.  I.]  METHOD.  191 

they  are  used  for  that  comprehensive  view  of  facts 
and  truths  in  the  particular  departments, 
or  in  the  whole  field  of  knowledge,  above  gcience  further 
set  forth.     Thus  we  speak  indifferently  Compared   and 

Defined. 

of  the  Science  of  Mind  and  of  the  Phi- 
losophy of  Mind,  of  Natural  Philosophy  and  Phy- 
sical Science.  But  the  words  are  often  used  with  a 
sort  of  contrast,  according  to  which  science  is  re- 
stricted to  the  domain  of  Physics,  and  Philosophy 
is  more"  particularly  referred  to  Metaphysics.  This 
is  especially  so  when  these  terms  are  used  alone, 
without  any  qualifying  adjunct.  Thus,  if  we  use 
the  word  Science  alone  and  absolutely,  we  usually 
mean  Physical  Science.  And  when  we  speak  of 
Philosophy  absolutely  and  eminenter,  we  mean  Me- 
taphysics, as  including  mind,  which  is  the  prime 
cause,  and  those  first  truths  of  Causality  and  Sub- 
stance, Time  and  Space,  which  variously  condi- 
tion being,  whether  body  or  spirit. 

12.  As  all  effective  thinking,  or  application  of  the 
laws  of  thought,  tends,  and  is  indispen- 

i  i       ,      ,  i  ,  .      ,«  r-       •  Logical  Method 

sable,  to  the  construction  of  science,  or  j,^^  Defini- 
thorough  knowledge,  so  Logical  Method  tion'    Division, 

and  Reasoning. 

in  every  department  of  inquiry  involves 

the  three  great   logical  processes  which  mutually 


192  LOGIC.  [Chap.  VII. 

supplement  and  complete  each  other.  Definition, 
which  unfolds  the  nature  of  the  science  according  to 
its  attributes  or  qualities :  Division,  which  unfolds 
it  according  to  its  extension  or  the  objects  it  includes : 
and  Reasoning,  in  which  we  either  guide  our  search 
for  facts  and  truth,  or  interpret  these  facts  by 
showing  what  can  fairly  be  inferred  from  them.  In 
regard  to  Definition  and  Division,  it  is  unnecessary 
to  expatiate  upon  them  here.  It  is  enough  to  refer 
the  student  to  the  principles  already  laid  down  on 
„  these  subjects.     It  is  only  necessary  to 

Importance     of  ■*  J  * 

Definition   and  add,  that  exact  Division  and  Definition 
are  of  the  utmost  moment  to  the  suc- 
cessful investigation  and  treatment  of  any  subject. 
We  will  now  fix  our  attention  on  the  application  of 
the  modes  of  reasoning  to  the  discovery,  elucidation, 
and  proof  of  the  truth,  in  regard  to  the  object- 
matter  so  marked  out  by  these  processes.    These  rea- 
sonings are  subject  to  different  conditions,  and  have 
a  different  cogency  and  force,  according  as  they  are 
applied  to  Necessary  or  Contingent  Matter. 
13.  The  former,  as  before  defined,  is  that  the 
,  opposite  of  which  the  mind  cannot  con- 

jNecessary    and      x  x 

Contingent  Dis-  ceive  without  intellectual  suicide.     The 
latter  is  that  whose  existence  is  Con- 


Sac.  II.]  METHOD.  193 

tingent,  and  the  supposition  of  whose  non-existence 
involves  no  contradiction  or  absurdity.  These  two 
kinds  of  truth  give  rise  to  the  two  orders  of  reason- 
ing, respectively  known  as  Demonstrative  and  Pro- 
bable, and  to  the  three  classes  of  Judgments  classed 
by  logicians  respectively  as, 

Sect.  II. — Problematic,  Assertory,  and  Apodictic 

Judgments. 

14.  The  two  former  apply  to  the  region  of  Con- 
tingent,* the  last  to  that  of  Necessary  truth.  This 
distinction  in  judgments  concerns  the  degree  of  cer- 
tainty in  the  connection  between  the  subject  and 
the  predicate. 

A.  The  Problematic  Judgment  is  neither  sub- 
jectively nor  objectively  certain ;  i.  e.  it 

J  .  .  Problematic 

is  not  certain  to  him  who  holds  it,  nor     Judgment  = 

!  r.  .,  Opinion. 

can   he    enforce    its    acceptance   upon 
others.     It  is  equivalent  to  mere  opinion. 

B.  Assertory  Judgments  are  true  and  certain  sub- 
jectively but  not  objectively,  i.  e.  sure     Assertory  = 
to  him  who  holds  them,  but  incapable     Faith* 

of  being  enforced  on  the  acceptance  of  others  of  a 

*  This  must  not,  however,  be  pressed  so  far  as  to  impugn  the 
necessary  existence  of  God. 

1<"  N 


194  LOGIC.  [Chap.  VII. 

different  moral  disposition.  Of  this  nature  is  belief 
or  faith,  especially  Religious  Faith.  Its  judgments 
are  sure  to  the  believer,  although  they  cannot  be 
enforced  upon  those  of  a  contrary  moral  disposition. 
C.  Apodictic  or  Demonstrative  Judgments  are 
subjectively  and  objectively  sure ;  sure 

Apodictic  Judg- 
ments necessa-  to  him  who  holds  them,  and  capable  of 

r  y  true.  being  enforced  upon  all  of  sane  mind, 

who  can  be  made  to  understand  them  and  the  evi- 
dence for  them.  Of  this  nature  are  the  truths  in 
Mathematics,  Logic,  and  some  primary  axioms  in 
Ethics  and  Metaphysics. 

15.  In   regard  to   reasoning   in   the   sphere   of 
necessary  truth  or  apodictic  judgments, 

Reasoning  from  J  *  J      ° 

Apodictic  Jndg-  little  need  be  said.      The  conclusions 

ments  snrei  r»     n  •         s*  i_    •    J  a„ 

of  all  reasoning  from  such  judgments 
to  others  founded  upon  them,  that  conform  to  the 
principles  of  the  syllogism  in  its  various  forms  as 
set  forth  in  formal  logic,  are  as  certain,  and  as  im- 
possible to  be  false,  as  the  premises.   The 

Its  power  in  the    n  -,.  r-o      i    n         »n      ±.     ±i 

Formal  Sciences  formal  sciences  afford  fine  illustrations 
illustrated    by  0f  the  achievements  of  the  logical  faculty 

Geometry. 

in  enlarging  our  knowledge,  without 
in  the  least  increasing  its  original  materials,  but  by 
simply   explicating  them.     The  whole  science  of 


Sec.  II.]  METHOD.  195 

Geometry  is  but  the  logical  unfolding  of  the  con- 
tents of  a  few  primary  axioms.  So  also  And  all  Mathe. 
of  the  entire  range  of  pure  Mathematics,  matics- 
and  of  pure  Logic.  All  necessary  and  a  priori 
truths,  intuitive  and  deductive,  afford  premises  for 
necessary  conclusions.  Thus,  from  the  Reasoning  from 
a  priori  truth  that  space  is  illimitable,  a  priori  truths. 
it  follows  that  it  is  immeasurable.  From  the  a 
priori  truth,  "  every  event  must  have  a  cause,"  and 
the  minor  premise,  "thunder  has  occurred"  (or 
been    an   event),   it   follows   that  this 

n  From  one  a  pn- 

thunder  must  have  had  a  cause.     Here  ori  and  one  Con- 

,i       tineent  premise. 

the  major  premise  is  a  necessary,  the 
minor  a  contingent  but  certainly  proved  event; 
and  the  conclusion  is  true,  with  a  necessity  condi- 
tioned on  the  truth  of  the  minor,  i.  e.  in  this  sense, 
with  a  conditional  necessity.  In  genuine  logical 
reasoning  the  conclusion  is  a  necessary  consequence 
of  the  premises.  In  proportion  then  as  they  are 
necessarily  true,  the  conclusion  is  so  likewise.  In 
this  we  have  the  type  of  all  purely 


196  LOGIC.  [Chap.  VII. 

Sect.  III. — Deductive  Seasoning. 

16.  This  also  applies  in  all  cases  of  Reasoning 

from  wholes  known  in  whatever  way, 

This  the  type  of  J 

Deductive  Rea-  whether  of  Extension  or  Intension,  to 
the  parts  included  under  them;  from 
Genus  to  Species,  and  individuals  under  them,  or 
from  the  marks  of  the  individual  or  species  to  the 
marks  of  those  marks.  So  far  as  we  have  any 
generic  truths,  propositions  or  judgments  established, 
whether  in  necessary  or  contingent  matter,  these 
furnish  premises  whence  we  can  reason  with  neces- 
sary certainty,  to  individuals  or  classes  contained 
under  them.     If  it  be  established  that, 

(Intensive  Syllogism) — "  Polyps  are  animals, 

And  that 

Animals  have  sensation, 

then  it  follows  of  necessity  that 

Polyps  have  sensation." 

Deductive  Reasoning  then  is  from  Generals  to 

Deductive  Eea-  Particulars — the  form,  as  we  shall  see, 
souing  is  from  of  nearl     all  demonstrative  and  abso- 

Generals  to  Par-  ^ 

ticulars.  lutely  conclusive  reasoning. 

17.  But  how  do  we  obtain   these   universal   or 


Sec.  IV.]  METHOD.  197 

Generic  Judgments  in  Contingent  Matter,  when  all 
that  we  know  originally  of  mind  is 

.i        .     -i.    .  f      ■•     «     .       ,i,  t        Whence     come 

the   individual  facts  that  come  under  Qenerai  judg. 

the  purview  of  consciousness,  and   of  ments  in  Con" 

tingent  Matter? 

matter,  what  are  cognized  through  our 
senses  ?  facts  too,  the  opposite  of  which  are  pos- 
sible, and  which  it  is  conceivable  might  not  be  re- 
peated beyond  the  sphere  of  experience  thus  far 
had  ?  From  the  fact  that  such  persons  as  we  have 
known  die,  how  do  we  reach  the  conclusion  that  all 
men  are  mortal  ?  From  the  fact  that  some  water 
is  composed  of  oxygen'  and  hydrogen,  how  do  we 
know  that  all  water  is  so  constituted?  This  brings 
us  to  reasoning  from  particular  facts  to  a  general 
law  or  truth,  which  is, 

Sect.  IV. — Induction. 

17.  This  is  the  principal  instrument  of  scientific 
progress,  and  of  all  advance  in  human 

By  Induction,  or 

knowledge,  except  through  Divine  Re-  reasoning  from 
velation,  within  the  realms  of  actual  nn 

7  G-enera. 

being.  For  this  is  a  region  of  facts,  Actual  beings 
objects,  phenomena  of  actual  existence  are  Indmduals> 
which  are  first  known  as  individuals,  and  might  or 

might  not  be,  according  to  the  good  pleasure  of  God. 

17* 


198  LOGIC.  [Chap.  VII. 

The  Formal  Sciences  and  Metaphysics  do  not  of 
Scope  of  Formal  themselves  discover  or  prove  any  actual 
Sciences.  being.     They  only  show  certain  neces- 

sary conditions  or  consequences  of  any  facts  of  actual 
being,  which  may  be  brought  to  light  by  the  other 
cognitive  powers. 

But  all  advance  in  the  knowledge,  and  especially 
.    the  scientific  knowledge  of  mind,  is  in 

All  progress  in 

Scientific  Know-  the  way  of  ascent  from  particular  facts 

bdng  Is^from  to  Seneral  laws-  Jt  proceeds  therefore, 
Individuals   to  from  what  we  know  in  some  cases,  to 

Classes,  . 

infer  that  the  like  is  true  in  all  similar 
cases.  This  is  induction  or  inductive  generalization. 
T  ,   a  Induction,  however,  is  more  than  Gen- 

Indnction  more  7  * 

than  Generaii-  eralization,  which  it  always  includes. 
There  may  be  generalization  without 
induction,  though  there  can  be  no  induction  without 
generalization.  Generalization  combines  in  a  class 
objects  having  similar  qualities,  and  denotes  them 
In  what  respect  by  a  class-name.  Induction  concludes 
it  is  so.  from  the  fact  that  some  of  a  given  class 

already  generalized  possess  some  given  property,  all 
others  of  that  class  possess  it — in  other  words,  that 
because  a  certain  mark  A  is,  in  some  cases,  attended 
with  a  certain  mark  B,  it  is  so  in  all  other  cases. 


Sec.  IV.]  METHOD.  199 

Thus,  from  the  fact  that  some  fire  tortures  living 
flesh  in  contact  with  it,  we  reason  in- 
ductively that  all  fire  will  do  it.     Here 
is  generalization  in  this  way,  and  to  this  extent,  that 
what  is  found  true  of  some,  is  extended  to  all,  that 
have  a  given  mark. 

18.  The  great  question  then,  in  regard  to  this 
class  of  cases,  which  needs  to  be  deter- 

The  great  ques- 

mined,  is,  when  are  we  warranted  in  tion   regarding 
taking  some  instances  that  have  come 
under  our  knowledge,  as  samples  or  accurate  repre- 
sentatives of  a  whole  class,  including;,  it 

°         What  are  tests 

may  be,  like  cases  innumerable  ?    What  or  crucial  in- 

,i  »■      «         l  •   i      v   .•         •  i    j_i  stanceSi 

are  the  criteria  which  distinguish  these 

crucial   instances   from   others   which  warrant   no 

such  inference? 

19.  There  is  the  test  of  a  complete  enumeration 
of  all  the  instances  or  individual  cases     simpie  Enu- 
composing  the  class  in  question.      If     deration. 
these  all,  without  exception,  have  the  property  in 
question,  then  it  of  course  belongs  to  the  whole 
class.     Thus,  if  the  season  of  greatest 

growth  is  in  May,  June,  July,  August, 
which  are  the  only  months  whose  names  are  with- 
out the  letter  r,  then  the  general  conclusion  follows 


200  LOGIC.  [Chap.  VII. 

with  absolute  certainty,  that  the  months  without 
the  letter  r  are  those  of  greatest  growth.  If  it  has 
been  found  from  actual  observation,  that  each  of 
the  planets  moves  in  an  elliptical  orbit,  then  it  is 
true  beyond  a  peradventure,  that  all  the  planets 
move  in  such  orbits.  This  is  what  Bacon  called 
Induction  per  simplicem  mumerationem,  by  the  mere 
enumeration  of  all  the  cases  involved. 

Why  this  is  Em- 
pirical   Indue-  It  has  also  been  named  Empirical  In- 
duction, because  its  compass  is  limited 
to  actual  experience,  and  it  detects  no  cause  and 
.  ,     .       .     establishes    no    law   reaching    beyond 

And  nnimport-  &  J 

ant.  such  experience.     It  is  therefore  com- 

paratively unimportant.     That  induction  alone  is 

Th  l  fr  Lt-  fruitf11!  which  enables  us  to  go  beyond 
fill  induction,  such  cases  as  have  fallen  within  our 
experience,  to  an  indefinite  number  of  like  cases, 
i,  e.  all  of  the  same  class  not  yet  brought  within 
the  range  of  our  experience. 

20.  In  order  to  this,  it  is  necessary  to  ascertain, 

Requisites  to  it.  not  only  the   empirical   fact,  that,   in 

A  Causal        such  instances  as  have  fallen  under  our 

gency'  cognizance,  the  phenomenon  in  question 

has  occurred,  but  that  there  is  a  causal  agency,  or 

other  uniform  concomitant,  connected  with   them 


Sec.  IV.]  METHOD.  201 

which  ensures  it,  and  which  attends  all  like  instances. 
Then,  when  it  is  settled  what  is  the  cause  or  mark 
of  any  given  phenomenon,  the  principle  that  like 
causes  produce  like  effects,  which  is  either  self-evi- 
dent, or  so  nearly  so  that  all  mankind  act  upon  it, 
induces  the  conclusion  that,  in  all  similar  cases,  we 
may  anticipate  a  like  phenomenon. 

21.  The  difference  between  such   an   induction 
and  that  which  is  purely  empirical,  per 
smvplicem,   emtmerationcm,  is  strikingly  gimpie  Enume- 

illustrated  in  the  second  example  of  the  ratioE  nitra- 
ted. 
latter- kind,  above  given,  which  was  the 

inductive  conclusion  that  all  the  planets  move  in 

elliptical  orbits,  from  observing  that  each  of  them 

moves   in   such   orbits.     This,  however,  of  itself, 

creates   only   a    moderate   presumption,   that   any 

planets  now  unknown  and  yet  to  be  discovered, 

move  in  such  orbits.     But  when  it  was  ascertained 

that  the   Centripetal   and   Centrifugal    Causal    Force 

Forces  act  jointly  on  all  the  planets,  and    Discovered. 

that  the  product  of  this  joint  action  is  an  elliptical 

orbit,  then  the  conclusion  was  indisputable,  that  all 

planets  observed  and  unobserved,  move  in  elliptical 

orbits. 

22.  What   then   are   the  Tests   of  such    Causal 


202  LOGIC.  [Chap.  VII. 

Agency,  or  other  equivalent  concomitant,  and  proof 

Tests  of  Causal  of  a  given  phenomenon?  The  proofs 
Agency,  etc.  that  a  given  object  or  agency  is,  or  con- 
tains in  itself,  the  cause,  or  invariable  concomitant  of 
a  given  effect,  so  that  we  are  warranted  in  asserting 
that  the  instances  observed  are  as  good  as  the  entire 
inductive Syllo-  class  of  like  instances?  The  Inductive 
gism.  Syllogism  naturally  falls  into  the  Third 

Figure.     Thus : 

"XYZ  have  polarity, 
XYZ  are  (represent  quoad  hoc)  all  magnets, 
.*.  All  magnets  have  polarity." 

It  may,  however,  be  put  more  awkwardly,  in  the 
First  Figure.     Thus : 

"XYZ  have  polarity, 
All  magnets  are  (represented  quoad  hoc  by)  XYZ. 
.*.  All  magnets  have  polarity." 

In  either  case  the  question  is,  when  do  the  parti- 

The  Question  re-  cular  cases  X  Y  Z  so  represent  the 
garding  it.  whole  class,  or  when  are  they  so  proved 
to  be,  or  to  contain  the  causes  or  uniform  con- 
comitants of  a  given  phenomenon,  that  they  fairly 
represent  the  whole  class,  and  warrant  a  universal 
inductive  conclusion  ? 


Sec.  IV.]  METHOD.  203 

1st  Criterion,  the  Method  of  Agreement. 
— If,  whenever  a  given  object  or  agency 

J. St    X6St  IS  tno 

is  present,  without  counteracting  forces,  Method  of 

™  .  i         i      ^i  •      Agreement, 

a   given    effect   is   produced,   there   is 
strong  ground  that  we  have  found  the  true  cause 
of  the  effect,  which  will  always  produce  it,  in  the 
absence  of  counteracting  forces.     Thus, 
it,  in   all   cases  ot   the   application  oi 
given  degrees  of  heat,  clay  hardens,  lead  melts,  and 
water  boils,  it  is  just  to  conclude  that  this  is  the 
real  cause  of  these  phenomena,  and  that  whenever 
it  is  applied  in  such  measure  to  these  several  sub- 
stances, they  will  re-occur.    It  is  to  be  borne  in  mind, 
however,  that  the  same  effect  may  pro- 

-,   n  too         ,  t  -t  Exception. 

ceed  from  different  causes.     In  order  to  game  effect  may 
determine   to   which   of   two   possible  pyoceed  from 

different  causes, 

causes  it  is  due,  in  any  given  cases,  the 
distinctive  indications  of  each  respectively  must 
be  sought.  This  is  usually  not  difficult.  The 
sensation  of  heat  may  arise  from  the  general  warmth 
of  the  weather,  from  an  artificial  fire,  from  exces- 
sive clothing,  or  from  fever.  It  is  usually  easy,  in 
view  of  all  the  circumstances,  to  determine  which. 
But  if  not,  unreal  causes  may  be  eliminated  by  the 
2d  Criterion  ;  the  Method  of  Difference. 


204  LOGIC.  [Chap.  VII. 

— This  is  given  when,  the  supposed   cause   being 
present  the  effect  is  present,  and  this 

2d  Test.    Me-      r  ... 

thod  of  differ-     being  absent  the  effect  is  wanting,  i.  e. 

unless  in  the  former  case  other  coun- 

xception.         ter-agents  are  present  to  neutralize  it, 

or  in  the  latter  to  produce  it.     Thus,  it  is  double 

proof  that  sound  is  the  result  of  vibra- 

Example.  . .  r,  . ,    i    i        .  i  , 

tions  oi   air   excited    by  the   resonant 

body,  if,  on  the  one  hand,  whenever  sound  is  heard, 
such  vibrations  are  found;  whenever  such  vibra- 
tions appear  sound  is  given  forth ;  and  if,  on  the 
other  hand,  a  bell  or  other  sonorous  body,  suspended 
and  struck  in  an  exhausted  receiver,  yields  no  sound. 
It  proves  that  the  contact  of  moisture  is  the  cause 
of  the  decomposition  of  animal  matter,  if,  whenever 
the  latter  occurs  such  moisture  is  present ;  if  dry- 
ness checks  or  arrests  it ;  and  if  salt,  which  prevents 
it,  acts  by  detaching  the  water  from  the  meats  which 
it  preserves.  If,  when  reason  is  present,  there  is 
accountability,  and  when  it  is  absent  there  is  none, 
then  it  is  a  condition  of  accountability. 

3d   Criterion — accounting  for  residual  varia- 
tions without  invalidating  the  proof  of 
3d  Test.  Eesid- 

ual    variations  the  supposed  cause.     Thus,  it  was  found 

accounted  for.       ^   ^^    trayeled    fagter   than    what 


Sec.  IV.]  METHOD.  205 

seemed  the  true  theory  of  its  law  of  velocity  allowed. 
It  was  suspected,  however,  that  the  rarefaction  of 
the  air,  arising  from  the  heat  produced  by  the  mo- 
tion of  the  sound,  accelerated  its  progress  to  this  ex- 
tent. Experiments  proved  this  conjecture  true, 
and  thus  confirmed  the  original  hypothesis.* 

*  The  following  striking  example  is  given  in  the  words  of 
Tlwmson's  Laws  of  Thought,  New  York  Edition,  pp.  262-3,  Chap. 
VII. 

"  In  Sir  Humphrey  Davy's  experiments  upon  the  decomposition 
of  water  by  galvanism,  it  was  found  that  besides  the  two  compo- 
nents of  water,  oxygen  and  hydrogen,  an  acid  and  an  alkali  were 
developed  at  the  two  opposite  poles  of  the  machine.  As  the 
theory  of  the  analysis  of  water  did  not  give  reason  to  expect 
these  products,  they  were  a  residual  phenomenon,  the  cause  of 
which  was  still  to  be  found.  Some  chemists  thought  that  elec- 
tricity had  the  power  of  producing  these  substances  of  itself;  and 
if  their  erroneous  conjecture  had  been  adopted,  succeeding  re- 
searches would  have  gone  upon  a  false  scent,  considering  galvanic 
electricity  as  a  producing  rather  than  a  decomposing  force.  The 
happier  insight  of  Davy  conjectured  that  there  might  be  some 
hidden  cause  of  this  portion  of  the  effect;  the  glass  vessel  con- 
taining the  water  might  suffer  partial  decomposition,  or  some 
foreign  matter  might  be  mingled  with  the  water,  and  the  acid 
and  alkali  be  disengaged  from  it,  so  that  the  water  would  have 
no  share  in  their  production.  Assuming  this  he  proceeded  to  try 
whether  the  total  removal  of  the  cause  would  destroy  the  effect, 
or  at  least  the  diminution  of  it  cause  a  corresponding  change  in 
the  amount  of  effect  produced.  By  the  substitution  of  gold  vessels 
for  the  glass  without  any  cbange  in  the  effect,  he  at  once  deter- 
18 


206  LOGIC.  [Chap.  VII. 

4th  Criterion.   Concomitant  Variations. — 
If,  as  the  amount  of  the  supposed  cause 

4th  Test.    Con-        '  rr 

comitant  Varia-  varies,  the  effect  varies  proportionally, 
it  is  strong  evidence  of  its  being  the 
real  cause.  "  That  the  column  of  mercury  in  the 
Torricellian  tube  was  counterpoised  by  a  column 
of  air,  was  proved  by  Pascal  when  he  caused  the 
instrument  to  be  carried  up  the  mountain,  and 
found  that  as  the  ascent  gradually  diminished  the 
height  of  the  column  of  air  above  it,  so  was  the 
column  of  air  it  was  able  to  sustain  diminished  in 
proportion." 

mined  that  the  glass  was  not  the  cause.  Employing  distilled 
water  he  found  a  marked  diminution  of  the  quantity  of  acid  and 
alkali  evolved;  still  there  was  enough  to  show  that  the  cause, 
whatever  it  was,  was  still  in  operation.  Impurity  of  the  water 
then  was  not  the  sole,  but  a  concurrent  cause.  He  now  conceived 
that  the  perspiration  from  the  hands  touching  the  instruments 
might  affect  the  case,  as  it  would  contain  common  salt,  and  an 
acid  and  an  alkali  would  result  from  its  decomposition  under  the 
agency  of  electricity.  By  carefully  avoiding  such  contact,  he 
reduced  the  quantity  of  the  products  still  further,  until  no  more 
than  slight  traces  of  them  were  perceptible.  What  remained  of 
the  effect  might  be  traceable  to  impurities  of  the  atmosphere,  de- 
composed by  contact  with  the  electrical  apparatus.  An  experi- 
ment determined  this ;  the  machine  was  placed  under  an  ex- 
hausted receiver,  and  when  thus  secured  from  atmospheric 
influence,  it  no  longer  evolved  the  acid  and  the  alkali." 


Sec.  V.]  METHOD.  207 

When  either  of  these  criteria  is  found,  free  from 
conflicting  evidence,  and  especially  when  several  of 
them  concur,  the  evidence  is  clear  that  the  cases 
observed,  are  fair  representatives  of  the  whole  class, 
and  warrant  a  valid  universal  inductive  conclusion. 

Sect.  V. — Hypothesis. 
23.  But  why  make  observations  and  experiments 
in  one  direction,  or  for  the  purpose  of  ^eas011  for  gy- 
testing  one  view  of  the  cause  of  given  P0thesl3- 
phenomena,  rather  than  any  other  ?     It  can  only  be 
because  the  mind  entertains  some  conjecture  or  sus- 
picion that  this   may  correspond  with   the  facts. 
Thus  it  is  led  to  institute  investigations 
and  trials  for  the  purpose  of  testing  the  sonabie  conjec- 
truth  of  this  conjecture.     Such  a  con-  ture  or  Tenta- 

•         t  t  tive  Theory. 

jecture  so  entertained  is  a  Scientific  Hy- 
pothesis, which  is  thus  but  a  provisional  and  tentative 
theory,  while  a  true  theory  is  a  proved  hypothesis. 
Such  hypotheses,  although  they  have  often  been 
abused,  by  the  premature  or  unwarrantable  assump- 
tion of  their  truth,  are  indispensable  to  effective 
progress  in  science.     Without  such  a 

r     a  Use  and  Neees- 

suide  and  stimulus,  all  observations  and  sity  of  Hypo- 
experiments  would  be  aimless,  and  com- 


208  LOGIC.  [Chap.  VII. 

monly  fruitless.  Indeed,  for  the  most  part,  they 
would  be  unattempted.  Investigations  so  guided 
have  led  to  nearly  all  the  great  achievements  of 
scientific  progress. 

24.  Some  confound  Theory  with  Hypothesis,  and 
accurate  writers  often  find  it  difficult  to 

How  far  Theory 

and  Hypothesis  use  them  so  as  to  avoid  all  shades  of 

are  synonymous.  .  -r>    ,  ,1 

synonymous  meaning.  But  neverthe- 
less, correct  use  points  towards  the  difference  we  have 
indicated.  Hypothesis  could  not  be  well  substituted 
for  Theory,  when  we  speak  of  Wells'  theory  of  dew, 
or  Dalton's  theory  of  definite  chemical  proportions, 
or  the  Newtonian  theory  of  universal  gravitation. 
And  yet  theory  is  often  used  for  hypothesis,  i.  e. 
for  an  unproved  doctrine  or  speculation,  or  a  tenta- 
tive and  provisional,  but  uncertain  explanation  of 
phenomena.  Thus  we  speak  of  Smith's  Theory  of 
the  Moral  Sentiments ;  the  exploded  phlogiston  and 
anti-phlogiston  theories.  Some  use  theory  for  a 
provisional  and  unproved  explanation  of  a  large 
group  of  facts.  This  however  is  but  an  hypothesis 
regarding  such  a  group  of  facts. 

Definition  f  ^n  regarc^  *°  *ne  distinction  be- 
some  Scientific  tween  Theoretical  and  Practical  Judg- 

Terms. 

Judgments.        ments,  and  other  Scientific  Terms,  we 


Sec.  -V.]  METHOD.  209 

quote    the    following    from   Thomson's   Laws   of 
Thought: 

"  Judgments  that  relate  to  speculation  only,  are 
called  Theoretical ;  those  which  refer  to  T  ,       .  _ 

7  Judgments  Tne- 

practice     are     Practical.      Judgments  oretical,  Practi- 

pn  l     TjpTn  on  ^i"Tfl~ 

that   require   or   admit   of   proof,   are  ble'    inaemon- 
called  Demonstrable;  those  which  are  strable- 
manifest  from  the  very  terms,  are  Indemonstrable. 
Thus  much  being  premised  we  can  define  certain 
subordinate  parts  of  a  science. 

An  Axiom  is  an  indemonstrable  theoretical  judg- 
ment.    A  Postulate  is  an  indemonstra-  ^iom    Postu- 
ble  practical  judgment.     A  Theorem  is  late> Tlieorem' 
a   demonstrable    theoretical  judgment. 
A  Problem  is  a  demonstrable  practical 
judgment.     A   Thesis   is   a  judgment      Thesis. 
proposed  for  discussion  and  proof  (but  with  Aris- 
totle it  sometimes  means  an  axiom  of  some  special 
science  or  disputation).     An  Hypothesis 
is  a  judgment  provisionally  accepted  as 
an  explanation  of  some  group  of  facts,  and  is  liable 
to  be  discarded  if  it  is  found  inconsistent  with  them. 
A  judgment  which  follows  immediately  from  an- 
other, is  sometimes  called  a  Corollary 
or   Consectary.     One  which    does    not 

18*  0 


210  LOGIC.  [Chap.  VII. 

properly  belong  to  the  science  in  which  it  appears, 
but  is  taken  from  another,  is  called  a  Lemma.  One 
Lemma.  which  illustrates  the  science  where  it  ap- 

ScMion.  pears,  but  is  not  an  integral  part  of  it  is 

a  Scholion." 

25.  The  great  distinction  of  Scientific  Genius  lies 
Chief  mark  of  chiefly  in  this  insight  which,  with  keen 
Scientific  gemus.  discernment  of  analogies,  anticipates  the 
truths  or  laws  of  nature,  and  devises  observations 
and  experiments  to  prove  or  disprove  them.  So 
Newton  suspected  that  the  same  force  which  causes 
the  falling  of  an  apple,  propels  all  matter,  and  pro- 
duces the  revolution  of  the  planets;  Franklin, 
that  lightning  is  a  discharge  of  electricity.  They 
proceeded  to  verify  these  hypotheses  by  experiments 
and  observations  which  proved  them.  While  the 
legitimate  use  of  hypothesis  is  thus  advantageous 
and  essential  to  science,  the  cautions  needful  to  be 
observed  to  prevent  the  abuse  of  it  are, 
Cautions  in  Ee-  A.  No  hypothesis  should  be  assumed 
5"  ■  t(\  I?\  to  account  for  what  can  be  otherwise 

thesis,    1,  Must 

be  needed.  accounted  for,  on  existing  and  known 
principles. 

B.  It  should  be  adequate  to  account 

2.  Adequate.       n      ,,         ,  .  ,. 

for  the  phenomena  in  question. 


Sec.  VI.]  METHOD.  211 

C.  The  facts  to  be  accounted  for  should  be  real 
and  not  imaginary,  as  the  question  be- 

fore  mentioned  of  Charles  II.  to  the  be  explained 
Koyal  society,  why  a  live  nsh  in  water 
would  increase  its  weight,  while  a  dead  fish  would 
not,  and  quite  perplexed  some  of  its  members,  until 
it  occurred  to  them  to  inquire  if  the  fact  were  so. 

D.  It   should    be    independent    of    -$0  subsidiary 
subsidiary  hypotheses  —  it  should  not    HvPotheses' 
require  other  hypotheses  to  account  for  itself. 

E.  It  should  not  be  assumed  to  be    To  be  accepted 
true  until  proved  to  be  so.  when  proved. 


Sect.  VI. — Analogy. 

26.  When  it  is  argued  from  a  known  resemblance 
between  objects  or  classes  in  some  known  Reasoning  from 


particulars,  that  they  resemble  each  Analogy  defined. 
other  in  other  respects,  this  is  reasoning  from 
analogy.  It  has  been  common  to  define  analogy  as 
a  proportion  between  objects.      When 

,-,     .     ,  ,  j         Example. 

we  reason  that   because  men  resemble 
animals  in  having  life  and  sensation,  they  therefore 
resemble  them  in  the  power  of  locomotion,  or  in 
the   grade   of  their   intelligence,  we   reason   from 


212  LOGIC.  [Chap.  VII. 

analogy,  or  the  relative  proportion  of  objects.*     It 
is  obvious  that  this  is  a  very  uncertain  argument, 

Has  only  a  pro-   and   can>   in   n0   CaSe>   rise   higher   than 

babie  force.  mere  probability.  This  probability  will 
be  weaker  or  stronger  according  to  circumstances. 
The  argument  for  future  retribution,  from  the  pre- 
sent evils  visited  upon  sin,  is  certainly  stronger  than 
the  argument  that  brutes  have  reason  because  other 
conscious  beings  have  it.  But  in  neither  case  is  it 
conclusive.  The  argument  from  analogy  may  be 
well    employed   to   add   a   cumulative 

May  strengthen  x      J 

other  argu-        force  to  other  arguments.      It  is  not, 

mentSi  ■,  .  i      ■  *»  •  >     1 /» 

however,  in  any  case  conclusive  of  itseli. 

27.  Its  most  important  service,  however,  is  in 

„         , , .      refutation  of  fallacious  arguments.     It 

Most  useful  in  » 

refutation.  often  has  in  this  way  a  powerful  nega- 
tive force.  Thus,  if  it  be  objected  to  the  doctrine 
of  future  punishment  that  the  infliction 
of  pain  is  inconsistent  with  the  benevo- 


Examples. 


lence  of  God,  this  argument  is  refuted  by  the  fact 

*  To  reason  from  Analogy,  is  to  reason  from  the  Intension  of 
that  to  which  it  relates.  To  reason  by  Induction  is  to  reason 
in  extension  from  one  or  some  objects  in  a  class  to  all  in  that 
class.  In  analogical  reasoning,  we  argue  from  a  resemblance  in 
some  qualities  to  a  resemblance  in  other  qualities. 


Sec.  VII.]  METHOD.  213 

that  God  does  inflict  pain,  or  so  order  and  permit 
events  that  it  is  undeniably  inflicted,  in  this  life. 
The  alleged  impossibility  of  the  future  life  and 
immortality  of  the  body  on  account  of  its  death,  is 
disproved  by  the  fact  that  in  all  nature  life  is 
evolved  from  death,  and  the  seed  which  we  sow 
"  is  not  quickened  except  it  die."     1  Cor.  xv.  36. 

Sect.  VII. — Categories. 
28.  These  are  summa  genera  of  predicables. 
Logicians  and  metaphysicians  have  Definition  of 
sought  to  give  complete  lists  of  these  Categories. 
summa  genera,  to  which  all  particular  predicables 
and  classes  of  predicables  might  be  referred.  It 
has,  however,  been  hard  to  find  any  such  exhaus- 
tive enumeration.  Says  Whateley,  "  The  Categories 
enumerated  by  Aristotle,  are  odaia,  Aristotle's  Cate- 
izbaoVy  Tidlov,  jrpoazc,  ~oi)y  trove,  xetadat,  Sories' 
e%£iv,  TtoiEiv,  Ttdayziv ;  which  are  usually  rendered, 
as  adequately  as,  perhaps,  they  can  be  in  our  lan- 
guage, substance,  quantity,  quality,  relation,  place, 
time,  situation,  possession,  action,  suffering.  The 
catalogue  (which  certainly  is  but  a  very  crude  one) 
has  been  by  some  writers  enlarged,  as  it  is  evident 
may  easily  be  done  by  subdividing  some  of  the 


214  .        LOGIC.  [Chap.  VII. 

heads ;  and  by  others  curtailed,  as  it  is  no  less  evi- 
dent that  all  may  ultimately  be  referred  to  the  two 
heads  of  substance,  and  attribute,  or  (in  the  language 
of  some  logicians)  accident."  Some,  however,  per- 
haps justly,  translate  e/£*v,  "  mode  of  action,"  in- 
stead of  "  possession."  Aristotle's  Categories  are 
rather  metaphysical  than  logical. 

29.  Kant's  celebrated  four  triplets  of  Categories 
Kant's  Cate-  are  certainly  ingenious,  and,  if  not  ab- 
gories.  solutely  exhaustive,  in  a  metaphysical 

view,  go  far  to  show  the  nature  and  a  'priori  basis 
of  the  several  logical  judgments.  According  to 
him  all  judgments  must  connect  the  predicate  with 
the  subject  so  as  to  involve  under  the  head  of, 

1.  Quantity.  2.  Quality.  3.  Relation.  4.  Modality. 

Unity,  Affirmation,     Substance  and  Accident,       Possibility, 

Plurality,    Negation,         Cause  and  Effect,  Eeality, 

Totality.      Limitation.      Action  and  Eeaction.  Necessity. 

It  may  be  observed  that  the  first  of  these  triplets 
corresponds  to  Singular,  Particular,  and  Universal 
Judgments;  the  second  to  Affirmative,  Negative, 
and  Kestrictive*  Judgments;  the  third  to  Categori- 

*  Restrictive  Judgments  "are  such  as  contain  a  negative  in  the 
predicate-conception,  e.  g.,  God  is  infinite.  The  human  soul  is 
immortal.     In  respect  to  their  contents,  they  are  negative ;  but 


Sec.  VII.]  METHOD.  215 

cal,  Conditional,  and  Disjunctive  Judgments;  the 
fourth  to  Problematic,  Assertory,  and  Apodictic 
Judgments. 

30.  Tables  of  Categories  are  almost  as  various 
as  the  writers  on  Logic  and  Metaphy- 
sics.    McCosh  gives  the  following  as 

a  provisional  summary  of  primary  judgments. 

1.  Identity  and  Difference.  5.  Quantity. 

2.  Whole  and  Parts.  6.  Resemblance. 

3.  Space.  7.  Active  Property. 

4.  Time.  8,  Cause  and  Effect. 

31.  J.  S.  Mill  in  his  Logic  gives  the  following 
classification    of    nameable    things   in 
the  spirit  of  the  Positive  Philosophy. 


J.  S.  Mill. 


1.  Feelings  or  states  of  consciousness. 

2.  The  minds  which  experience  these  feelings. 

3.  The  bodies  or  external  objects  which  excite  certain  of 
these  feelings,  together  with  the  power  or  properties  whereby 
they  excite  them. 

in  respect  to  form,  they  are  affirmative.  Logically  considered, 
therefore,  they  belong  to  the  class  of  affirmative  judgments. 
These  judgments  are  also  called  infinite,  or  more  properly  indefi- 
nite, because,  by  means  of  a  predicate  involving  a  negative,  the 
subject  is  transferred  from  the  sphere  of  definite  conception  to 
that  of  indefinite  conception,  a  sphere  to  which  it  does  not  pro- 
perly belong." — Gerhart's  Philosophy  and  Logic,  p.  214. 


216 


LOGIC. 


[Chap.  VII. 


4.  The  successions  and  coexistences,  the  likenesses  and  un- 
likenesses  between  feelings  and  states  of  consciousness." — 
Logic,  I.  111. 

32.  Thomson   (Laws   of  Thought,   p.  315)  just 
attempts  the  following : 


TABLE  OF  THE  CATEGORIES. 


ID 
fcJD 


J2  ' 

3 

S3 

.i-H 

o 

c 
o 

o 


Substance 


'  Quantity 


Attribute     i  Quality 


.  Kelation 


of  Time 

of  Space 

of  Causation 

of  Composition 

of  Agreement  and  Eepug- 

nance 
of  Polar  Opposition 
of  Finite  to  Infinite. 


Sec.  VIII.]  METHOD.  217 

Sect.  VIII. — Harmony  and  Co-ordination  of  Sciences. 

33.  As  the  application  of  scientific  method  to  any 
given  and  mutually  related  set  of  phenomena  or 
truths  develops  a  science  of  these  facts,  like  the 
Science  of  Botany,  Anatomy,  Ethics,  etc.,  so  many 
of  these  sciences  are  related  to  each  other  as  Genus 
and  Species.  Thus  Ornithology,  Piscatology,  etc., 
under  Zoology.     Various  attempts  have 

i  i      ,        t       •/»     ,i       n  ■  Classification 

been  made  to  classify  the  Sciences  so    and    uutuai 

as  to  show  their  Mutual  Harmony  and    Ha™ony   of 

.  the  Sciences. 

Interdependence.    It  is  plain  that  they 

might  be  logically  divided  and  sub-divided  from 
various  stand-points,  which  have  been  taken  ac- 
cording to  the  respective  aims  and  purposes  of  the 
authors.  Thus  they  may  be  divided  into  the 
Speculative  and  Practical,  or  the  Phy-  gpeculative  and 
sical  and  Metaphysical,  or  the  Formal  Practical,  etc. 
and  Material,  etc.,  with  their  respective  subdivisions. 
Attempts  of  this  sort  have  often  been  made,  with 
considerable  success  and  utility. 

34.  Compte  and  the  positive  school  of  philoso- 
phers, however,  amidst  their  enormous  errors,  have 
unfolded  a  scheme  of  classification  and  co-ordination 
among  the  sciences,  at  once  beautiful  and  fruitful, 

19 


218  LOGIC.  [Chap.  VII. 

which  has  commanded  wide  acceptance  among  those 
who  have  attended  to  the  subject. 

Starting  with  Descartes'  suggestion,  that  the 
order  of  arranging  the  sciences  should  be  from  the 
simplest  to  the  more  complex,  he  adopts  the  fol- 
lowing, which  at  once  commends  itself  by  its  sim- 
plicity, naturalness,  and  beauty,  and  which  we  give, 
as  we  find  it,  in  a  form  most  available  for  our  pre- 
sent purpose,  in  Thomson's  Laws  of  Thought,  pp. 
316-19. 

"  Mathematics,  or  the  science  of  quantity,  is  at 
once  the  most  simple  in  its  elements  and  the  most 
general  in  its  application,  entering  more  or  less  into 
all  the  sciences  of  nature,  and  constituting  almost 
the  whole  of  that  which  comes  next  it  in  the  order 
of  dependence.  Astronomy,  or  the  science  of  the 
heavenly  bodies,  is  the  application  of  mathematical 
truths  to  the  laws  of  matter  and  motion ;  matter  and 
the  motions  of  material  bodies  being  the  new  con- 
ception which  belong  to  this  science.  Physics,  being 
the  science,  or  rather  group  of  sciences,  which  is 
conversant  with  the  general  laws  of  the  world,  so 
far  as  they  relate  to  beings  without  life  or  organiza- 
tion, would  come  next ;  and  it  imports,  in  addition 
to  the  conceptions  of  Astronomy,  those  of  light,  of 


Sec.  VIIL]  METHOD.  219 

heat,  of  sound,  of  electricity,  of  magnetism,  and 
many  others.  Chemistry  would  rank  next,  which 
is  the  science  of  the  decomposition  and  combinations 
of  the  various  substances  that  compose  and  surround 
the  earth.  Next  in  order  of  complexity  would  rank 
Physiology,  founded  on  the  additional  conception 
of  vegetable  and  animal  life.  To  this  would  suc- 
ceed Anthropology,  or  the  science  of  man's  nature; 
and  to  this  Social  Science,  which  ascertains  the  laws 
that  govern  men  when  combined  in  cities  and  na- 
tions. Each  of  these  departments  may  be  divided 
into  many  branches;  as  Physics  into  Acoustics, 
Optics,  Electricity,  and  the  like;  or  Social  Science 
into  Morals,  Politics,  Political  Economy,  Law,  and 
the  like. 

"  On  comparing  scientific  works,  differences  in  the 
mode  of  teaching  the  same  subject  become  appar- 
ent. In  one  the  pure  theory  of  Astronomy  is 
presented;  in  another  the  striking  features  of  its 
historical  progress  as  a  science,  with  speculations  on 
the  historical  sequence  of  the  phenomena  themselves ; 
in  a  third  the  practical  applications  of  which  the 
science  admits  in  respect  to  the  comfort  and  progress 
of  mankind.  This  threefold  mode  of  treatment 
runs  through  all  the  sciences;  and  in  a  table  of 


220  LOGIC.  [Chap.  VII. 

them  might  well  be  expressed.  The  classification 
would  thus  embody  all  that  is  valuable  of  another 
system  of  classes,  that  according  to  the  purpose 
towards  which  the  science  was  directed. 

"A  classification  which  advances  on  Descartes' 
principle,  from  the  more  simple  to  the  more  com- 
plex subjects,  which  commences  from  the  notions  of 
extension  and  quantity,  and  proceeds  through  ma- 
terial things,  up  to  living,  intelligent,  and  moral 
agents,  ought  to  coincide  with  the  order  in  which 
the  sciences  themselves  have  reached  maturity. 
And  this  it  certainly  does.  Mathematics  had  made 
good  its  ground  when  astronomy  was  yet  in  its 
infancy;  physics  began  to  obtain  a  sure  footing 
later  than  either •  whilst  the  sciences  which  relate  to 
life  are  still  very  immature;  and  some  of  the  main 
problems  of  social  science  are  yet  matter  of  contro- 
versy even  in  our  own  days. 

"There  is  besides  a  general  correspondence  between 
this  classification  and  the  order  in  which  the  various 
objects  of  science  came  into  being.  The  heavenly 
bodies  were  first  appointed  their  paths  in  the  celes- 
tial spaces;  then  the  surface  of  our  earth  was  pre- 
pared for  living  creatures ;  then  they  were  created 
after  their  kind,  and  man  the  last.     The  social  life 


Sec.  VIII.] 


METHOD. 


221 


of  man  grew  up  last  of  all,  when  his  race  was  mul- 
tiplied on  the  globe ;  and  ever  as  new  elements  ap- 
pear, the  conditions  of  society  are  being  modified 
even  to  the  present  time." 
Hence  emerges  the  following 


"classification  of  the  sciences. 

Group.  Mode  of  Treatment. 

I.  Mathematics Theoretical.     Historical.     Applied. 

II.  Astronomy Theoretical.  Historical.  Applied. 

III.  Physics Theoretical.  Historical.  Applied. 

IV.  Chemistry Theoretical.  Historical.  Applied. 

V.  Physiology Theoretical.  Historical.  Applied. 

VI.  Anthropology.... Theoretical.     Historical.    Applied. 
VII.  Social  Science Theoretical.     Historical.     Applied. 

V , 

Eeligious  Philosophy." 
19* 


APPENDIX. 


APPENDIX  A. 

EXAMPLES     FOR     PRAXIS. 

ffl^  The  following  examples  may  be  used  for  'practical  exercise  in 
Conceptions,  Judgments,  and  Reasonings  of  all  kinds.  In 
analyzing  Syllogisms,  let  the  student  complete  them  when  un- 
finished, and  point  out  their  kind,  whether  Categorical  or 
Hypothetical;  if  the  former,  give  their  Mood  and  Figure;  if 
the  latter,  show  whether  they  are  Conditionals,  Disjunctives,  or 
Dilemmas.  Mark  the  Enthymemes,  Sorites,  Prosyllogisms, 
and  Episyllogisms.  In  all  cases  show  ivhether  the  Syllogism 
is  valid  or  invalid,  and  if  invalid,  indicate  the  kind  of  Fal- 
lacy. 

1.  Body  is  extended  substance, 
This  inkstand  is  a  body, 

.*.  It  is  extended  substance. 

2.  Plants  are  bodies  with  organization, 
Potatoes  are  plants. 


223 


224  APPENDIX. 

3.  Animals  are  bodies  having  organization  and  sensation, 
Frogs  have  organization  and  sensation. 

4.  Bodies  having  organization,  sensibility,  and  reason  are 

men, 
The  poets  are  men. 


»•••••«•• 


5.   X  Y  Z,  are  ruminant, 

X  Y  Z,  are  (as  good  as)  all  horned  cattle. 


••••••••a 


6.  Quadrupeds  are  animals, 

Worms  are  animals. 

i 

7.  Oaks  are  vegetable, 
Oysters  are  not  oaks. 


8.    Beasts  are  animals, 
Birds  are  not  beasts. 


••••••••• 


9.   These  emigrants  are  either  Scotch,  Irish,  or  German, 
They  are  not  Germans. 


•••••*•« 


10.  These  people  are  patriots  because  they  are  free. 

11.  If  the  classics  teach  how  to  produce  wealth  they  ought 

to  be  studied, 
They  do  not  so  teach. 


<•*.... 


EXAMPLES  FOB  PRAXIS.  225 

12.  If  we  can  prevent  what  occurs  we  ought  not  to  fret 

about  it, 
If  we  cannot  prevent  what  occurs  we  ought  not  to  fret 

about  it, 
But  either  we  can  or  cannot  prevent  it. 


•      •*<*••••> 


13.  A  Christian  nation  is  brave, 
A  brave  nation  is  free, 
A  free  nation  is  happy. 


•••••••» 


14.  A  plane  triangle  is  a  rectilineal  figure  having  three  sides, 
A  plane  triangle  is  A  B  C. 


•      •••••*••• 


15.  All  these  trees  make  a  thick  shade, 
This  catalpa  is  one  of  these  trees, 

.*.  It  makes  a  thick  shade. 

16.  Whatever  study  gives  knowledge  relative  to  either  of 

the  three  learned  professions  ought  to  be  a  part  of 
liberal  education ; 
Geology  and  Mathematics  do  not  give  such  knowledge, 
.*.  They  ought  not  to  be  studied. 

17.  If  all  men  are  liars  then  nothing  can  be  proved  by 

human  testimony ; 
But  some  things  can  be  proved  by  human  testimony, 
.*.  No  men  are  liars. 

18.  Typhoid  fever  is  epidemic, 
Because  A.  B.  and  C.  have  it. 

P 


226  APPENDIX. 

19.  An  inflated  currency  promotes  national  prosperity,  be- 

cause it  enables  persons  to  make  rapid  fortunes. 

20.  What  we  eat  grows  in  the  fields  or  is  the  flesh  of  animals, 
Cooked  food  is  what  we  eat,  1 

.'.  Cooked  food  grows  in  the  fields  or  is  the  flesh  of  animals. 

21.  The  rumor  that  A.  B.  has  committed  a  given  crime  is 

universal,  for  I  heard  it  from  Mr.  A  and  Mr.  B. 

22.  If  we  say  the  Baptism  of  John  was  from  heaven  we  con- 

demn ourselves  for  not  believing  him  ; 
If  we  say  it  was  of  men,  the  people  will  stone  us ; 
But  we  must,  if  we  say  any  thing,  confess  it  was  from 

heaven  or  of  men ; 
.*.  If  we  say  any  thing,  we  must  either  condemn  ourselves, 

or  the  people  will  stone  us.     Luke  xx.  4-6. 

23.  Some  flowers  are  (all  the)  tulips, 
All  flowers  are  beautiful, 

.*.  All  the  tulips  are  beautiful. 

24.  All  false  religions  have  sustained  their  claims  bv  alleged 

miracles, 
Christianity  sustains  its  claims  by  alleged  miracles ; 
.*.  It  is  a  false  religion. 

25.  The  hour-hand  can  never  overtake  the  minute-hand  of  a 
clock,  because  while  it  is  passing  to  the  point  where  the  minute- 
hand  is  at  any  given  moment,  the  latter  will  have  advanced 


EXAMPLES  FOR  PRAXIS.  227 

some  distance :  and  when  the  former  has  passed  over  this  dis- 
tance the  minute-hand  will  have  advanced  still  further ;  and 
so  on  ad  infinitum. 

26.  This  man  has  an  excellent  character  because  he  belongs  to 
an  excellent  church,  as  appears  from  its  being  composed  of 
such  excellent  men. 


27.  He  who  is  most  hungry  eats  most, 
He  who  eats  least  is  most  hungry, 

.'.  He  who  eats  least  eats  most. 

28.  If  the  taking  of  an  oath  to  discharge  our  duty  tends  to 
secure  its  performance,  then  it  ought  to  be  repeated  in  refer- 
ence to  every  duty  of  life  ;  if  it  does  not,  then  the  civil  oaths 
administered  are  superfluous.  But  one  or  the  other  of  these 
are  true.  .*.  The  oaths  commonly  administered  are  superfluous, 
or  they  should  be  repeated  in  connection  with  every  duty  of 
life. 

29.  No  man  is  rich  who  is  not  content, 

No  miser  is  content  (i.  e.  every  miser  is  one  who  is  not 
content), 
.*.  No  miser  is  rich. 

30.  Men  can  live  without  animal  food,  and  they  can  live 

without  vegetable  food,  as  has  been  often  demonstrated, 
But  all  food  is  either  animal  or  vegetable, 
.*.  Men  can  live  without  food. 

31.  He  who  calls  you  a  man  speaks  truly, 
He  who  calls  you  a  fool  calls  you  a  man, 

.*.  He  who  calls  you  a  fool  speaks  truly. 


228  APPENDIX. 

32.  Useful  studies  ought  to  be  encouraged, 

Logic,  since  it  helps  us  to  reason  accurately,  is  such, 
.'.  It  ought  to  be  encouraged. 

33.  X  Y  Z  have  polarity, 

X  Y  Z  are  (as  good  as)  all  magnets, 
for  polarity  appears  wherever  magnets  are ;  it  disappears  when 
they  are  withdrawn,  unless  other  polar  forces  are  present,  and 
it  increases  with  the  power  of  the  magnet ; 
.*.  All  magnets  have  polarity. 

34.  Some  men  of  genius  are  (all)  the  poets, 
Some  poets  are  melancholy. 


35.  The  mind  is  a  thinking  substance, 
A  thinking  substance  is  a  spirit, 

A  spirit  has  no  composition  of  parts, 

That  which  has  no  composition  of  parts  is  indissoluble, 

That  which  is  indissoluble  is  immortal, 

Therefore  the  mind  is  immortal. 

36.  Protagoras  engaged  to  teach  Euathlus  the  art  of  pleading 
for  a  large  reward,  one  half  to  be  paid  at  once,  the  other  half 
when  the  latter  should  have  gained  his  first  cause  in  court. 
After  a  short  time  Protagoras  sued  Euathlus.  for  the  unpaid 
moiety,  enforcing  his  claim  by  the  following  Dilemma: 

If  the  case  is  decided  in  my  favor,  the  sum  will  be  due 
to  me  according  to  the  finding  of  the  court ; 

If  it  is  decided  in  your  favor,  the  sum  will  be  due  to  me 
according  to  our  contract, 


EXAMPLES  FOR  PRAXIS.  229 

But  it  must  be  decided  either  in  my  favor  or  yours. 
.'.  Whether  I  gain  or  lose  the  cause  I  shall  be  entitled  to 

the  reward.  * 
Euathlus  thus  answered . 
If  I  gain  the  cause,  nothing  will  be  due  you  according  to 

the  decision  of  the  court, 
If  I  lose  it  nothing  will  be  due  you  according  to  our 

contract ; 
But  I  shall  either  gain  or  lose  it, 
.*.  In  neither  case  shall  I  pay  you  the  reward. 

37.  A  policy  which  promotes  the  national  wealth  ought  to 

be  adopted ; 
But  the  education  of  the  people  increases  their  wants 
and  expenditures,  and  therefore  does  not  increase 
national  wealth ; 
.'.  It  ought  not  to  be  adopted. 

38.  All  is  not  gold  that  glitters, 
Tinsel  glitters, 

.'.  It  is  not  gold. 

39.  If  there  had  beer,  a  law  that  could  have  given  life,  then 

verily  righteousness  should  have  come  by  the  law, 
But  righteousness  did  not  come  by  the  law." 

•    •       #••••••••  ' .   X  ,'  (  I  ,    111*     _-  1  , 

*  The  fallacy  here  is  that  the  Disjunction  is  incomplete.  There 
is  another  horn,  viz  :  that  Protagoras  had  no  cause  of  action,  be- 
cause before  the  bringing  of  this  suit,  Euathlus  had  no  case  in 

court.     See  Chap.  V.,  29. 
20 


230  APPENDIX. 

40.  Poets  are  men, 
Orators  are  men. 


41.  Plants  are  bodies  with  life,  and  without  consciousness, 
Geraniums  are  such  bodies. 

42.  All  trees  bearing  acorns  are  oaks, 
Some  trees  do  not  bear  acorns. 

43.  All  men  are  rational  animals, 
Apes  are  not  men, 

/.  They  are  not  rational  animals. 

44.  Some  men  are  orators, 
Some  bipeds  are  (all)  men, 

.*.  Some  bipeds  are  orators. 

45.  The  following  answer  was  given  to  Pyrrhus'  assertion 
that  nothing  can  be  certainly  known  : 

If  you  certainly  know  this,  your  assertion  is  disproved, 
If  you  do  not  certainly  know  it,  you  have  no  right  to 

affirm  it, 
But  you  either  do  or  do  not  know  it, 
Therefore  your  doctrine  is  untenable. 

4G.  Most  people  are  careless, 

Most  people  are  destitute  of  perfect  health. 

47.  It  is  almost  certain  that  C.  D.  is  a  true  witness  because 
there  is  a  probability  amounting  to  f  that  he  saw  and  ob- 


EXAMPLES  FOR  PRAXIS.  231 

served  correctly  what  he  testifies  about,  and  another  proba- 
bility of  f  that  he  would  tell  the  truth  if  he  did  know  it." 

What  is  the  probability  that  B.  B.  wrote  a  certain  anony- 
mous letter,  where  the  separate  probabilities  are, 
From  chirography,  £, 
From  the  sentiments,  i,  and 
From  his  known  meanness  of  character,  \. 


APPENDIX   B. 

SYLLOGISTIC     NOTATION. 

1.  Various  methods  have  been  adopted  to  represent  to 

the  eye  the  different  forms  of  the  Syllogism, 
Meaning  of  Syl-     an(i  ^  reia^ons  0f  thought  respectively  in- 

t,ion,  volved  in  them.     This  is  done  through  linear 

diagrams  analogous  to  the  figures  of  Geom- 
etry. It  greatly  assists  the  mind  in  discerning  at  a  glance 
the  quantity,  the  mutual  relation,  and  the  quality  of  the 
different  terms  and  judgments  of  the  syllogism,  together 
with  its  figure  and  mood.  One  of  the  most  celebrated 
schemes  of  notative  symbols  is  that  by  means  of  circles  in- 
vented by  Euler,  upon  which  we  have  already 

Euler's  Method      ,  ,,  «  ,    .,,     ,     ,. 

v   «■   i  drawn  tor  purposes  or  casual  illustration. 

(See  Chap.  V.  13.) 

2.  Three  circles  are  employed  to  denote  respectively  the 
Major,  Minor  and  Middle  Terms.  Affirmative  judgments  are 
symbolized  by  the  total  or  partial  ?^clusion  of  the  circle  signi- 
fying the  subject  in  that  which  stands  for  the  predicate. 

Negatives  are  signified  by  the  total  or  partial  exclusion 
of  the  former  from  the  latter. 

The  following  diagram,  in  which  A  B  and  C  denote  re- 
spectively the  minor,  middle,  and  major  terms,  represents, 
232 


8YLL 0  GISTIC  NO  TA  TION. 


233 


1.  The  moods  A  A  A.    2.  AEE.     3.  A  1 1.    4.  E  I  0,  all 

of  the  First  Figure. 


1.  Barbara. 


2.  Celarent. 


3.  Darii. 


4.  Ferio. 


Of  course,  this  method,  mutatis  mutandis,  is  applicable  to 

the  other  figures.     This  clearly  and  beautifully  represents  the 

Syllogism  according  to  extension,  as  also  the  distribution 

or  non-distribution  of  different  terms. 
20* 


234  APPENDIX. 


NOTATION   BY  STKAIGHT   LINES. 

4.  According  to  this  scheme,  a  horizontal  straight  line 
denotes  a  term  distributed.  The  letters  S,  P,  or  M  attached, 
indicate  that  it  is  respectively  minor,  major,  or  middle  term. 

S 

P 


Dots  are  used  to  signify  an  undistributed  term  as  noting 
its  indefiniteness. 


M 


Any  definite  portion  of  an  undistributed  term  is  indicated 
by  a  line  not  dotted  inserted  in  one  that  is  dotted.  Thus  in 
the  judgment  "men  are  mortal,"  &  e.  "some  mortals," 
mortal  is  undistributed.  But  we  take  that  definite  portion 
of  it  which  is  co-extensive  with  the  class  man.     Thus : 

p mortal. 

S men. 

Affirmative  judgments  are  symbolized  by  lines,  one  above 
the  other — the  former  being  the  predicate,  the  latter  the 
subject.  Negative  judgments  are  represented  by  parallel 
lines  drawn  so  that  one  is  not  under  the  other.     Thus : 


S 


To  complete  the  syllogism,  of  course  three  lines  must  be 
employed  to  represent  the  three  terms  and  judgments  in 
their  quantity  and  other  relations. 


SYLL  0  GISTIC  NO  TA  TION.  235 

P  

M  . 

S . 


This  represents  A  A  A,  of  Fig.  1.    Thus : 

All  horses  are  quadrupeds, 
All  Shetland  ponies  are  horses, 
.".  All  Shetland  ponies  are  quadrupeds. 

If  there  be  one  negative  premise  in  the  Syllogism,  it  can 
be  thus  represented.  The  following  is  E  A  E,  Celarent, 
of  Fig.  1. 

P 

M 

S 


No  M  is  P, 

All  S  is  M, 
.*.  No  S  is  M. 

Substitutive  Judgments  are  indicated  by  two  equal  and 
parallel  lines.     Thus : 

P 

S 


Judgments  of  Logical  Division  or  Colligation  (chap.  II.  43) 
may  be  expressed  thus : 

-      .  .       P x y z  P 

Division,  Colligation, 

S  S x  —  v z 


236  APPENDIX. 


THE   HAMILTONIAN   NOTATION. 

5.  Quite  the  most  expressive  and  complete  system  of 
Notation,  and  one  of  his  important  contributions  to  Logic, 
is  that  invented  by  Sir  William  Hamilton.  It  is  so  con- 
trived as  to  exhibit,  at  a  glance,  all  the  characteristics  of 
the  valid  Syllogism,  both  according  to  intension  and  exten- 
sion, in  all  the  figures.  This  is  done  by  means  of  lines, 
wedge-shaped  in  the  figured  Syllogism,  and  of  uniform  length 
and  breadth  in  the  unfigured  Syllogism,  and  in  all  substitu- 
tive judgments,  these  latter  lines  denoting  the  perfect 
equality  of  subject  and  predicate. 

6.  The  wedge-shaped  figure  or  line  denotes  a  judgment — 
its  thick  end  the  subject  of  extension  which  is  contained 
extensively  in  the  predicate :  its  thin  end  the  subject  of  in- 
tension, or  predicate  of  extension,  which  is  contained  inten- 
sively in  the  other.  Most  of  what  follows  is  so  well  put  in 
Bowen's  Logic,  that  we  transfer  it  with  little  modification. 

"As  the  employment  of  letters  following  upon  each  other 
in  the  same  alphabet  might  suggest  that  one  was  invariably 
subordinated  to  the  other,  instead  of  being  its  subordinate 
in  one  Quantity  and  its  superordinate  in  the  other,  Hamil- 
ton uses  for  the  Extremes  the  Latin  C  and  Greek  r,  each 
being  the  third  letter  in  its  own  alphabet;  as  usual,  M 
stands  for  Middle  Term.     Thus : 

is  read,  C  and  r  are  equal. 

may  be  read  in  two  ways ;  Extensively,  C  is  included  under 


SYLL  0  GISTIC  NO TA  TION.  237 

r  ;  Intensively,  vis  included  in  C: — or,  in  the  usual  manner, 
C  is  r,  and  r  is  C,  merely  remembering,  without  saying  so, 
that  Extension  is  signified  in  the  former  case,  and  Inten- 
sion in  the  latter. 

7.  ''Negation  is  indicated  by  a  perpendicular  stroke 
drawn  through  the  line,  thus:  ■— { — .  The  line  without 
this  stroke  may  be  regarded  as  the  Affirmative  Copula;  with 
the  stroke,  as  the  Negative  Copula.  A  colon  ( : )  annexed 
to  a  Term  shows  that  it  is  distributed,  or  taken  universally; 
a  comma  ( , )  so  annexed,  that  it  is  undistributed  or  Parti- 
cular. When  a  Middle  Term  has  a  colon  on  the  right,  and 
a  comma  on  the  left,  it  is  understood  that  it  is  distributed 
when  coupled  in  a  Judgment  with  the  Term  on  the  right, 
and  undistributed  when  coupled  with  the  other. 

8.  "A  line  drawn  beneath  or  above  three  Terms  indicates 
the  Conclusion  (or  the  Copula  of  the  Conclusion)  deduced 
from  the  two  Premises  which  those  Terms  constitute.  In 
the  Second  and  Third  Figures,  since  there  may  be  two 
equally  direct  or  immediate  Conclusions,  they  are  represented 
by  two  such  lines,  the  one  above,  and  the  other  below  the 
Premises.     Thus : 

This  is  a  Syllogism  in  the  Second 
r 
Figure,  which  may  be  read  in  either 

of  the  following  ways. 

Extensively.  Intensively. 

Some  C  is  some  M ;  All  M  is  some  T; 

Some  r  is  all  M ;  Some  M  is  some  C; 

.*.  Some  r  is  some  C;  or  .'.  Some  C  is  some  T;  or 

.'.  Some  C  is  some  r.  ,\  Some  r  is  some  C. 


938  APPENDIX. 

C,  — — «,  M:  — I"- •:  r  "This  is  a  negative  Syllogism 
j— —  in  the  First  Figure,  which  may  be 
read  in  either  of  the  following  ways;  but  in  either  way,  it 
has  onty  one  direct  or  immediate  Conclusion,  though  a 
Second  Conclusion  may  be  obtained  from  it  indirectly,  by^ 
converting  simply  the  proper  or  direct  Conclusion. 

Extensively.  Intensively. 

Some  M  is  some  C ;  No  M  is  any  r ; 

No  r  is  any  M ;  Some  C  is  some  M ; 

No  r  is  some  C ;  or,  Some  C  is  not  any  r ;  or, 

indirectly.  indirectly. 

Some  C  is  not  any  r ;  Not  any  r  is  some  C. 

9.  "The  following  diagram  presents  the  whole  Hamil- 
tonian  doctrine  of  Figure,  together  with  the  distinction 
between  the  Analytic  and  the  Synthetic  order  of  enounce- 
ment.  After  the  explanations  which  have  been  given,  it  will 
be  easily  understood. 

"As  a  Judgment  has  been  designated  by  a  line,  a  Syllo- 
gism, which  is  a  union  of  three  Judgments,  is  appropriately 
typified  by  a  triangle,  a  union  of  three  lines,  of  which  the 
base  represents  the  Conclusion,  and  the  other  two  lines,  the 
Premises.  As  the  direction  of  the  arrows  indicates,  we  may 
proceed  either  in  the  usual  or  Synthetic  order,  from  the 
Premises  to  the  Conclusion,  or  in  the  reverse  order,  which 
is  Analytic,  from  the  Conclusion  to  the  Premises.  As  there 
is  no  valid  reason  for  always  placing  the  Major  Premise 
first  in  order,  the  diagram  shows  that  either  Premise  may 
have  precedence  in  this  respect,  so  that  what  has  been 


SYLLOGISTIC  NOTATION. 


239 


called  the  Fourth  Figure  is  here  identified  with  the  Indirect 
Moods  of  the  First. 


*      *      * 

"The  Unfigured  Syllogism  is  properly  represented  as  in- 
cluding all  the  others,  as  any  Syllogism  of  either  Figure  may 
be  easily  expressed  in  this  form.  In  like  manner  the 
triangle  representing  the  First  Figure  is  made  to  include  the 
two  typifying  respectively  the  Second  and  Third,  as  either 
of  the  latter  may  be  readily  reduced  to  the  former.  And 
again,  the  essential  unity  of  the  Syllogistic  process,  and  the 
unessential  nature  of  variation  by  Figure,  are  appropriately 
signified  by  a  single  triangle  comprehending  all  the  varieties 
of  form. 


240  APPENDIX. 

"The  double  Conclusions,  both  equally  direct,  in  the 
Second  and  Third  Figures,  are  shown  in  the  crossing  of  two 
counter  and  corresponding  lines.  The  Direct  and  Indirect 
Conclusions  in  the  First  Figure  are  distinctly  typified  by  a 
common  and  by  a  broken  line;  the  broken  line  is  placed 
immediately  under  the  other,  and  may  thus  indicate  that  it 
represents  only  a  reflex  of  —  a  consequence  through  the 
other." 

10.  It  will  be  remembered  that  the  four  fundamental 
judgments  hitherto  recognized  by  logicians,  viz.,  A  E  I  0, 
yield  sixty-four  conceivable  moods.  Excluding  from  these  all 
that  are  invalid  as  offending  against  the  laws  of  the  syllogism, 
only  eleven  moods  remain  that  are  valid  in  the  fourteen  syl- 
logisms of  the  first  three  figures,  or  nineteen,  if  the  fourth 
figure  be  recognized.  But  Hamilton,  as  we  have  seen,  recog- 
nizes eight  judgments,  adding  to  the  four  already  named,  U 
Y  i  oi.  The  possible  combinations  of  these  are  five  hundred 
and  twelve.  Of  this  number,  however,  only  thirty-six  will 
bear  the  tests  of  valid  syllogisms,  of  which  twelve  are  affirma- 
mative  and  twenty-four  negative.  Thus,  on  this  system, 
each  affirmative  mood  has  two  corresponding  ones  that  are 
negative,  as  each  of  its  premises  may  be  made  negative. 
Since  each  of  the  moods  on  this  system  can  be  put  in 
either  of  the  three  figures,  there  arise  three  times  thirty- 
six,  or  one  hundred  and  eight  valid  syllogisms  in  the  several 
figures.  The  changes  in  the  different  figures,  however,  are 
for  the  most  part  unessential  and  insignificant.  The  follow- 
ing table  by  Hamilton  exhibits  the  eight  judgments  re- 
cognized by  him,  very  ingeniously  in  their  relative  strength, 


SYLL  0  GISTIC  NO  TA  TION. 


241 


in  which  A  signifies  a  term  distributed,  I  a  term  undistri- 
buted, f  an  Affirmative,  and  n  a  Negative  copula.  A  par- 
ticular is  accounted  weaker  than  a  universal,  and  a  negative 
weaker  than  an  affirmative. 


Best. 


Worst. 


{ 


-5 
6 


1.  Afa. 

2.  An. 

3.  Ifa. 
Ifi. 
Ini. 
Ina. 
Ani. 


All  are  all. 
All  are  some. 
Some  are  all. 
Some  are  some. 
Some  are  not  some. 
Some  are  not  any. 
Not  any  is  some. 


-8.  Ana.    Not  any  is  any. 


"  With  these  explanations,  the  following  list  of  the  twelve 
valid  Affirmative  Moods  in  each  of  the  three  Figures,  and 
the  twenty-four  valid  Negative  Moods  in  the  First  Figure, 
all  expressed  in  the  Hamiltonian  notation,  will  be  found 
intelligible,. 

11.  "In  this  Table,  the  Quantity  of  the  Conclusion  is 
marked  only  in  the  cases  already  considered,  wherein  the 
Terms  obtain  a  different  Quantity  from  that  which  they 
held  in  the  Premises ;  accordingly,  when  not  marked,  the 
quantification  of  the  Premises  is  held  as  repeated  in  the 
Conclusion.  The  symbol w^— ',  placed  beneath  a  Conclusion, 
indicates  that,  when  the  Premises  are  converted,  the  Syllo- 
gism remains  in  the  same  Mood ;  ^><C.  shows  that  the  two 
Moods  between  which  it  stands  are  convertible  into  each 

other  by  converting  their  Premises.     The  Middle  Term  is 
21  Q 


242 


APPENDIX. 


THE  HAMILTONIAN  ANALYSIS  AND  SCHEME 

TABLE    OF    SYLLO- 

A.    AFFIRMATIVE   MOODS. 


B 


i.  C 
ii.  C,- 
iii.  C  ,- 

iv.  C:" 

v.  C,; 

vi.  C,- 


vii.  C 


viii.  C. 


ix.  C: 


x.  C: 


xi.  C:- 


xii.  C  , . 


Fig.  i. 


M 


C  :, 


:M 


,,r       c,a 


— — — ^g 


X 

,M 


M 


X 

,  M: 


M: 


M: 


M, 


X 

,M 


M, 


X 

,  M 


.,r       C:, 


.,r       c 


«,r      c,« 


i,r      c 


r      c 


':  r 


EB3 


I:  T        C  :i 


i,  r        C  :, 


r      c, 


Fig.  ii. 


:M 


W^ 


:M: 


^rJ 


:M, 


,M: 


:M, 


X 


,M 


:M 


X 


M 


:M, 


X 


,M: 


':  r 


i:  r 


»,  r 


eaear 


i:  r 


i:  r 


HOBH 


X 


,M: 


».-r 


Note. — A.  i.  and  ii.  arc  Balanced.   B.  The  other  moods  arc  Unbalanced.  Of  these, 


SYLL  0  GISTIC  NO  TA  TION. 


243 


OF  NOTATION— FIGURED  SYLLOGISM 

GISTIC    MOODS. 
A.   AFFIRMATIVE   MOODS. 
Fig.  in. 


[IjJi  >PU|.  .  I-...— 

C  :  ,i ;  M  : 


E3H 


c,- 


■3BB 


V«W 


W<- ' 


M, 


X 


B.   NEGATIVE   MOODS. 


ra  C,- 
[b  C 


«a  :  M  , i— ■,  T 


iii.  and  iv.  are  unbalanced  in  terms  only,  not  in  propositions:  Hip  rest  in  both. 


244  APPENDIX. 

said  to  be  balanced,  when  it  is  Universal  in  both  Premises. 
The  Extremes,  or  Terms  of  the  Conclusion,  are  balanced, 
when  both  alike  are  distributed ;  unbalanced,  when  one  is, 
and  the  other  is  not,  distributed.  Accordingly,  of  the 
Moods,  in  this  Table,  numbers  I.  and  II.  are  balanced  as 
respects  both  terms  and  propositions ;  in  III.  and  IV. ,  only 
the  terms  are  unbalanced;  in  the  remainder  both  terms 
and  propositions  are  unbalanced." 


• 

Date  Due                          , 

'  &    V 

1 

^j*00* 

g-p#l^ 

• 

f) 

BC71.A88 

Manual  of  elementary  logic 


Princeton  Theological  Seminary-Speer  Library 


1    1012  00008  2828 


